I don't think it's impossible, no. Would it be a lot of work? Yes.
I think a good alternative is leasing, this way you can get some experience. Maybe you should lease a horse that isn't necessarily a lesson horse...a horse that isn't as 'dead broke', so to speak. This way you will get some experience, but a trainer/someone can guide you and you won't be in it alone. Then you'll gain some knowledge, but you may find out THAT is too much work & you may say screw it, I want a horse that is trained already.
I'll be honest, when I first got my horse (she's a 5yr old OTTB), she was VERY green. I've always ridden difficult horses/greener horses, but I never actually trained any myself. She didn't even know how to lunge, it took a lot of time and patience. I spent months on end doing just groundwork with her, then it transferred to the saddle. I eventually hit a plateau with the training, and I decided to reach out to a really, really good trainer & she helped me a TON with her. She has like over 30 years of experience and is an amazing horsewoman. There are things I know I wasn't capable of teaching my horse (I accepted that, there is ALWAYS something new to learn). While she still needs work of course, she has made huge improvements since I got her.
It's your choice, but you don't want to bite off more than you can chew.
Ride more, worry less.