The answer boils down to a belief that the early New Testament church somehow CHANGED the day of rest God himself initially made (Genesis 2:1-3) to Sunday. If this is the case, then we should find amble proof of it in the Bible.
Even if we searched day and night we would not find ANYWHERE in God's word any statement that clearly teaches he changed His day of rest and going to church to Sunday. We also would not come across any statements by Jesus that the Eternal has and would require a NEW day of rest for those who believe in Him. Our search would also lack ANY teaching of the apostles that specifically names the first day as the new Bible Sabbath. One of the primary ways used to justify such worship is to show that what occurred in the early church on this day MUST mean they had some sort of worship service on it, thereby confirming the change in days.
So, let us take a look at the places in the New Testament where Sunday shows up to see if this day became the new time for the church to worship upon. Unfortunately, according to Strong's Concordance, the word "Sunday" never appears. Those who wrote in the first century A.D. did not refer to the days of the week like as we do (e.g. Monday, Wednesday, etc.). They referred to it by the phrase "first day of the week." Our study will be relatively brief since this phrase occurs only EIGHT times in the New Testament (Matthew 28:1, Mark 16:2, 9, Luke 24:1, John 20:1, 19, Acts 20:7 and 1Corinthians 16:2).
The initial visit to the tomb
The first reference, in time sequence, we will look at is in the book of Matthew.
1. Now late on the Sabbath, as the first day of the weeks was drawing near, Mary Magdalene and the other Mary came to observe the sepulcher (Matthew 28:1, Holy Bible a Faithful Version throughout)
Days in the Bible begin at sunset. The seventh or Sabbath day ran from sunset Friday to sunset Saturday. Matthew 28:1 is simply telling us that two "Marys," about the time the Sabbath was ending (just before sunset), went to check on Jesus' tomb. There is no support here for going to church on what we define as Sunday, since this visit happened several hours before midnight Saturday!
A day of work
Four of our eight references to the first day of each week, none of which reference a church meeting, can be looked at together, since they all refer to events that occurred early on a particular Sunday.
2. And very early on the first day of the weeks (Sunday morning), at the rising of the sun, they were coming to the tomb . . . 9. Now after Jesus had risen, early the first day of the weeks He appeared first to Mary Magdalene (Mark 16:2, 9)
1. Now on the first day of the weeks (Sunday morning) . . . Mary Magdalene (a woman who had demons cast out of her by Christ) came early to the tomb . . . (John 20:1)
56. And they (women who had seen where Jesus' tomb was located - verse 55) returned to the city, and prepared spices and ointments, and then rested on the Sabbath . . . 1. Now on the first day of the weeks (Sunday morning) . . . bringing the spices that they had prepared (which were prepared on the Friday after the crucifixion, Luke 23:56 - 24:1)
The references to the first day in Mark 16:2 and John 20:1 merely note that certain people came to Jesus' tomb around sunrise. Mark's reference in verse 9 tells us that sometime right after Mary Magdalene came to the tomb that Jesus appeared to her. Note, however, something interesting. The books of Mark and John were both written in 42 A.D., twelve years after Jesus death and resurrection. Yet, more than a decade after Christ's ascension, they do not call the Sunday on which these events occurred the "Lord's Day" or state that what happened occurred on the day believers go to church! There is absolutely no mention that the first day should be hallowed or that what occurred should be commemorated (e.g. Easter).
Luke 23:56 tells us that certain women prepared spices and ointments for Jesus' body. Then, instead of immediately applying what they made to Christ's body, they RESTED "on the Sabbath according to the COMMANDMENT." This can only be referring to the fourth of God's Ten Commandments (Exodus 20:8 - 11) which states no work should be done on the seventh day (sunset Friday to sunset Saturday). Anointing a body was considered work. This means the women finished their preparations just before sunset Friday, rested Friday sunset to Saturday sunset, then went to anoint Jesus' body as soon as enough light was available to do so (early Sunday).
Luke's account, written almost thirty years after the events he describes occurs, hides an obvious fact. The work needed to anoint Jesus, which in obedience to God could not be done Friday sunset to Saturday sunset (the seventh day of the week), COULD be performed on the first day (Sunday)! This means in 59 A.D., when Luke wrote his gospel, the first day of each week was NOT considered holy and a time for church but just another work day!
Gathering to hide
Our sixth reference to the first day of the week, or Sunday, is found in John 20.
19. Afterwards, as evening was drawing near that day, the first day of the weeks, and the doors were shut . . . (John 20:19)
Was the early church celebrating the Sabbath on this day? Were they gathering to commemorate the death of Jesus that had just occurred a few days before? No! They gathered in a certain place and shut the door out of FEAR of the Jews who had just instigated Jesus' murder!
Did Paul conduct services?
7. Now on the first day of the weeks, when the disciples had assembled to break bread (a phrase commonly used to denote eating a meal), Paul preached to them and because he was going to leave in the morning . . . (Acts 20:7)
This certainly seems like a Sunday worship service with Paul preaching the message. Note, however, that the apostle spoke when he did because he would leave the assembled group IN THE MORNING. Paul was giving this message after sunset (lamps were needed in the room - verse 8) on a Saturday (which is the beginning part of the first day of the week). He wanted to teach and encourage this group of believers in Troas as much as possible before he left to continue his missionary journey.
Was there a collection?
Let us look at the final location in the New Testament where the term "first day" (referring to Sunday) is used.
2. Every first day of the week, each one is to put aside FOOD at home, storing up whatever he may be prospered in . . . (1Corinthians 16:2)
Notice that the above verse does NOT mention a collection being taken up for the ministry or for evangelism. This is NOT a freewill offering made in order to help the local church pay its bills. Things were collected for the SAINTS (verse 1). What was being collected? Not money but FOOD! Where was it being collected? At HOME! Paul was encouraging the Corinthians to help their poor brethren in Judea, who were suffering from a severe drought, with food. Paul also mentions this relief effort to the church in Rome (Romans 15:25-26, 28).
The Bible does not contain a shred of evidence that shows that God, Jesus or early New Testament leaders CHANGED the day of worship from Saturday to Sunday. Scripture does not support conducting church services on any day but the seventh. For information on how the interplay of the Roman Empire, Jews and religious politics led to worshipping God on a day different than what the fourth commandment say, we highly suggest reading the book From Sabbath to Sunday.