Yes! A good loan officer will offer you a good rate the first time, but rates are negotiable. I would specifically ask your loan officer what you could do to get a lower rate. One way to lower your rate might be to put more money down, take less money out if it is a cash-out refinance, or you can always pay discount points to get a lower rate. Whatever you do, make sure you communicate to your Loan Officer on what your goals and expectations are with your rate. Make sure you are working with a mortgage professional and not just someone trying to make a quick buck.
Rates are also changing much more rapidly than they did several months ago. If you like the rate that you are getting quoted I would suggest locking it in right away. If you wait just a few minutes you could see that rate you like go up, or down. Typically the pain of seeing a rate go up far outweighs the joy of it going down. The old saying goes…“ if you like it, lock it.”