your body is still recovering.
a vagina is not a hole which is "tight" or "not". It is a collapsed tube which opens to allow penetration - thats' why you need a speculum to see a cervix.
if you're turned on, your vagina will respond to accommodate whatever you want to bung in there. If you are not, well, it won't.
You are very, very early postnatal. As in, you have no hope in hell of getting the same sexual response as you had pre-natally. Get some lube, and lashings of it. And, relax. Your baby a month old, give yourself a break.
Hurrah for wanting to be back in the saddle. That doesn't mean that everything is going to be the same as it was - you get a check at the GP at 6 weeks for good reason. TBH, it can take months to settle down.
Relax, use lube, have a wank, do your pelvic floor exercises, see how you go. Mainly though relax. A finger up a vag a few weeks after giving birth is not a good indicator of how a saddle's going to fit.
Seriously, you'll be fine. Try feeling less obliged to do much more than sleep and eat. I don't mean to be flippant, but, am serious, you are only baby steps into baby days. Relax, tell your partner to have a wank, empty the dishwasher, take the baby between midnight and 6am, give you a neck rub - for a month, and then, hop on.