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Rambam Sefer Hamitzvos negative command 153 says
We are forbidden from eating tevel, i.e. produce from which the terumos1 and ma'asros have not yet been separated.
Is there a comparable prohibition of eating produce before bikkurim (first fruits) have been separated? Would such produce be “tevel”?
Let's not forget the next prohibition on the Rambam's list (#154):
The 154th prohibition is that we are forbidden from giving the agricultural gifts out of order; rather, we must give them in the proper order.
Separating Terumot and Maaserot before separating Bikkurim violates one of the 613 Torah commandments (Mishna Terumot 3:6-7). So in practice your question is rarely relevant.
The Mishna in Bikkurim (2:3,5) list that one of the differences between Bikkurim and Teruma/Maaser is that only the latter אוסרים את הגורן prohibit the grain. Rambam there in his commentary explains:
הוא שאסור לאכול דבר מן הגורן עד שיוציאם ד״ל התרומה והמעשר לפי שהוא טבל ואינו כן בבכורים
It is forbidden to eat from the pile (of produce) until one removes them, the Teruma and Maaser that is, for it is Tevel; but it is not so regarding Bikkurim.
Some explain that particular Mishna differently, but I don't think anyone disputes this halachic point. No mention is made of Bikkurim in Rambam's presentation on the prohibition of eating Tevel (Maachalot Asurot 10). Moreover in Bikkurim 2:19 Rambam cautions against separating Bikkurim from impure produce because there is no point to doing so, implying there is no prohibition on consumption to be lifted.
