Considering getting a puppy with a baby since I’ll be at home.. can it work?

I lost my dog unexpectedly when I was pregnant and while I love my baby so much I still have a big dog-shaped hole in my heart.

We did a trial run with an adult shelter dog but unfortunately it wasn’t a good fit; he tried to crawl across some furniture to get to where we were sitting with our crying baby, and while we do have a fenced-in yard, we were worried he’d jump the fence due to an “escape artist” history. Fortunately the shelter took him back and he was promptly adopted by another family. While I’ve always been more in favor of rescues and adult dogs, I realized the safest thing (aside from waiting) might be getting a puppy (probably a lab) and training him alongside my child. I fully plan on installing a baby/puppy gate and giving the puppy his own “zone”- the laundry room with a dog door leading to a covered patio and yard.

Part of wanting to do this sooner rather than later is that I’m taking a year or so off to be a SAHM and finish online school (which is fairly flexible), so I’ll have more time to train a puppy than I will once I return to the work force.

I’ve seen this mostly advised against, but I really feel like it’s either now or several years down the road. Is there a way to make it work with a lot of patience and intentionality? Is it really going to be as bad as people say? What can make it work?

My baby is currently almost 4 months, but I’m considering waiting til he’s about 6-8 months before getting a puppy