If you are patient, roster spots open up all through the spring season and beyond - even throughout the summer.
Patience may be the best path to follow because you want - in theory - to find the highest level of play consistent with getting lots of playing time.
Too many freshman players get placed in top leagues only to find that they get a handful of at-bats scattered over the season (while their teammates get several hundred). (Pitchers are different; they keep getting appearences because most staffs get worn down - which can be good or bad depending on their performance.)
If a freshman has a decent freshman college season, there will be spots for him in the right leagues. My son's team brought in players who were not on the original roster starting on the first day of the season and kept bringing in players until the last week of the season. Some brought in on temp contracts were offered season contracts when they performed adequately.