Shalom Lchvod Harav! I heard that the Be’er Moshe held that the first time one uses a keili they don’t need to toivel it I would love a source.
The Rema Shulchan Aruch Y:D 120-16, that in retrospect if someone used a kli without prior tevilah, b’dieved the food is not prohibited from eating. He does not say that we have one free chance. Sorry to say but what you heard is fake news, and an unfounded (but unfortunately prevalent) rumor. In fact Horav Saul Yochanan Schwartz (The Debrecener Rov’s son in law) was asked about this and he said that his grandfather never said such a thing and to say something like that would be similar to saying that a nida is permitted once.
Having said that, it could be that this rumor is based on a mistake, and people are mixing up the fact that some poskim say that an aluminum foil pan, which is meant to be used only once does not need tevila. Possibly this got mixed into saying that it can be used once. Wherever the mistake is coming from.