If he's muscling everything, I don't know why you would think he'll be tapping you soon. If anything, he's going to tire himself out like that and be easy pickings after just a few minutes of fruitlessly trying to muscle you around. If you have sound fundamentals, its easy to play defensive guard and let him burn himself out.
If you've been training for 2.5 years, I'm sure you've seen bigger stronger guys get owned by much smaller guys. BJJ is about efficient technique, period. Strength obviously helps, but it's WAY WAY less efficient if you don't have sound technique to go with it.
And don't be intimidated by a strong new guy. Look at him as a challenging new training partner who's going to help you learn to use clean technique. It's not a competition and the more you get your ass kicked in practice, the more you learn and the better you get.