Convey 2 meanings in one sentence correctly [closed]

You can put "while only being in his sophomore year," in the beginning of the sentence as an introductory dependent clause so that it becomes much clearer that you want to emphasize that Tom still managed to qualify despite being a sophomore.

While only being in his sophomore year, Tom was the first ever student from Jacksonville University to qualify for the prestigious math competition.

You can also do the following:

Tom, despite being only a sophomore, was the first ever student from Jacksonville University to qualify for the prestigious math competition.

The trick here, for me, is to put the modifying clause as close to the subject/object as possible to avoid any confusion on which word or words are actually being referred to.