ANSWER: We will tackle your initial question first before getting to the meaning of sowing seeds and seed time. Firstfruit is a term used in the Bible to describe the first fruit of the first harvest. God commanded His people to present the first fruit of the land to the Levitical priesthood (Deuteronomy 26:2). Since Levites did not receive any land when the children of Israel received their inheritance in Canaan, God provided a way for them to be supported through the other tribes. God commanded ancient Israel to offer the firstfruit of their harvest to him in gratitude of the blessings they received (Exodus 23:19, 34:26, Ezekiel 44:30, etc.)
The Firstfruit of a harvest plays an important role in the celebrating of God's annual Feast days. On the day after the weekly Sabbath during the festive season known as the Days of Unleavened Bread, the priest waved barley before God (Leviticus 23:9 - 11). On the day of Pentecost (which is also known as the Feast of Firstfruits), fifty days later, two loaves made of fine flour were waved before God as his offering (Leviticus 23:17, 20). This marked the end of the grain (first) harvest and the beginning of the fruit harvest in Israel. On the first day of the Feast of Tabernacles in the Fall, Israel was commanded to offer the firstfruit of their produce and juices to him (Exodus 22:29, see also Numbers 18:12 - 13).
When we come to the New Testament Pentecost takes on a deeper spiritual meaning. Pentecost becomes the "birthday" of the New Testament church as God gives His Holy Spirit with signs and wonders (Acts 2:1 - 4). All people who are truly called out of this world, who have repented of their sins and have in them God's Holy Spirit, are considered by the Father to be his Firstfruit of the salvation of man.
To sow a seed simply means to plant a seed. The word of God uses this as a metaphor to describe the concept of working to achieve something positive. The Bible often uses symbolism associated with agricultural production because it was such an important part of ancient people's daily life, unlike the majority of people today. In one of Jesus' parables he uses the analogy of someone sowing seeds, and what can happen to the seeds afterwards, to teach about the different responses people will have regarding the gospel message (Luke 8:5 - 15).
Your mention of seed time, in your question about the term firstfruit, refers to the time when the environment, temperature and season are appropriate for the placing of seeds in the ground for their best success of growing. Growing up on a farm we spoke of seedtime as the time when the earth was warm enough and moist enough from the early spring rains to best guarantee the "sprouting" of the seed once it was placed in the ground. Otherwise, it would simply lie buried in the soil and die.
Springtime is the time of seeds. It is the time when life springs forth from the earth. We could associate "seed time" with the time of planting (Isaiah 60:21, 61:3).
Spiritually, we could say that when God places his Holy Spirit in us at the time of our repentance and baptism, it is a spiritual seed, the "beginning" of spiritual life within us. However, we can't let that "seed" just sit there and not grow, or it will die. We must water the "seed" of the Holy Spirit with continued bible study and prayer. We must put into practice every word of the teachings of the ENTIRE Bible to allow the Holy Spirit to grow in us.
So, when the time of the spiritual harvest comes, at the second coming of Jesus Christ, those who are true Christians will be the firstfruit of God's incredible salvation plan for man. Thank you for your question about the harvest and what sowing seeds means in the Bible.