Yes, my rescue was exact same way. Even a perfectly housetrained dog, will often have accidents in first weeks, it's nerves, and uncertainty, (whether you can read dog language to catch that in your dog or not, it is a rare dog who is put into brand new home, with brand new strangers, and relaxes in first weeks)
and the lack of courage to ask you anything, like "let me out"---or they don't know how to ask yet.
New dogs are on "company manners" for many weeks. Some dogs aren't even sure where the "bathroom" IS ha ha!!
{{EDIT---SORRY, i got you mixed up with someone else, YOU have baby dog, ohhh. Baby dogs take a lil while, ha ha, yeah, they do. They don't quite have the self control yet. Sounds like you are doing right things, though!!}}
So, i took him out on leash EVERY TWO HOURS, every 2 hours, and once again, very late at night, (and first night or two, also during night)
and very very early in the morning.
I cleaned up the messes, and did not scold. ever.
I praised him in slow calm voice whenever he'd peed or pooped outside, and gave a treat..
Overtime, i made note of which times he peed or pooped, and began, slowly, to stop some of the less useful outings.
Also, my dog does better to pee on a walk. He just does. If i put him in yard, he pees one time.
If i walk him, he pees and pees many times, gets way more empty.
Plus, walking is so relaxing and satisfying to upset dogs anyway, so really, i should say, i walked him eveyr 2 hours, even if only to the corner and back.
Overtime, we discovered his schedule, and where he liked to go best,
and then just walked him at those times.