It's so painful to practice when your fingers feel like they're slowly being sawed :'(
I would expect it to take as long as two months to build up callouses that make it comfortable, and up to six months to have the firmest callouses.
I recommend my students practice every day and also don't try to practice for hours and hours every day. Just half an hour a day is enough to get started.
I think the discomfort is testing how much you love it. If you can get past the discomfort, you'll probably be a guitarist for life.
I agree with everything Todd Wilcox said but want to add... (but can't comment yet...)
I started playing over 30 years ago and have restarted playing about 15 times, so been through this process a lot. Although people talk of the callouses and I when I first started they did feel like hard pads on the fingertips, but they don't have to be, but the extent of these and the ability to play without pain is also about how much pressure you put on the strings.
When learning to get your fingers into weird positions you may find yourself pressing hard to keep your fingers in place. Be aware of this and work on keeping your fingers close to the fret wire, as it will help reduce the pressure needed. Test each chord shape to see how little pressure it needs before it buzzes, you'd be suprised.
If your string action (height of your strings above the frets) is too high you will need more pressure and more clearance to move your fingers, this will increase the pain! Get your guitar setup properly, just a few mm change in action can turn a trip wire fret board into a lead master piece. It's also worth learning how to setup you're own guitar, setting the action at the nut and saddle even level frets. A properly tuned machine will sing!
Last thing to check is the string gauge you are using, it could be too heavy, try a gauge down, it won't solve it but it may help and it's good to try different strings.
If you know all this, done it and it doesn't help then as Todd said it's testing how much you love it... you have to give a little to get a little... or a lot.