Getting a new passport for a newborn? Traveling in 8 weeks

Hi all, I searched the subreddit but not sure if the older posts apply to my situation.

We just had a newborn and plan to travel to Canada in August. I’m trying to get him a passport, but the post office is booked out for 3-4 weeks. I’m afraid by then it will be too late to have it returned on time.

However, to get one expedited at the Mickey Leland building, you need to show that you are traveling within two weeks (which we are not). Therefore my question is… what’s the best way to get a new passport at this time? I don’t really wanna wait until two weeks before our trip to get it done. Thanks!