This tummy time has me really amazed. Do not know anything about it (raised my child a long time ago). However one thing I do know and there,s very valid research in the US about it. Babies under 3 months of age should NOT be put to sleep on their tummy. The recommendation, made during years and years (decades) to put them to sleep on their tummy to avoid suffocation and sudden crib death was all WRONG. Sometime in the 90,s, american doctors tried with two groups of babies, to put them to sleep as always (tummy down) or tummy up, for the first months. They were large groups. The amount of crib deaths in the group sleeping tummy down was so much bigger than in the other group that they discontinued the study and reversed their position: babies must sleep tummy up. They cannot move their necks well, and cannot get easily rid of reflux, etc. And when I had my daughter, I did try to put her tummy down and she hated it, even though she supported her head on her neck very well from day one, and the upper back too. So much she hated it that she actually "tried" to roll sideways (but could not). Therefore I decided to trust her (scared about going "against the norm") and when I read about the research many years later I was glad of it.
So I suggest that children 3 months or younger may have a very good reason to "hate tummy time", a survival reason to hate it, and that doing it for short times on your belly would be better, and safer. As for trying to crawl, doing anything positive about it seems very premature before four/five months (they are not normally ready till about 6/8 months although there will always be exceptions). Unless, of course, baby loves it. My daughter could support herself seated at 4 months, when she was ready to crawl she did it from the sitting position, like other children here have done.
And she did have "tummy time" the natural way (without my knowing of such recommendation or worrying about her neck....could not worry, she was competent from day one): lying on my belly, with me not even lying down entirely many times, it is just that you support her with your arms to see her beautiful face, make noises, she responds, you let her lie on your breast/belly....all these things that are done naturally after feeds, etc.