My dd could recite the alphabet very young. It made for some extremely cute home videos! But was otherwise useless as she hadn't "learned the alphabet" she was just making the noises having heard me sing it to her. She could also sing a number of songs in French. She just had a very sticky memory. It was a lot more meaningful when she could recite entire stories we read together as I knew she understood those, I always found the alphabet a hollow achievement.
So unless you are going to be teaching from an ABC book to actually recognise the letter shapes then don't bother, and don't worry in the slightest. You could teach a child to recite by rote basically ANYTHING if you repeat it and make it a game or song or regular thing you repeat over and over. Up to you whether you want to focus on the alphabet.
In any case at school they don't care so much about learning letter names Ay Bee See Dee, they use phonics to learn to read. So you may be better off teaching phonic sounds as a first step.
Counting and shapes and colours are in my opinion different as it is something you can actually learn in context and are useful. My son has learned colours from shouting out all the colours of the cars we see as we go about our daily lives ( silver, white and black were learned before purple or green!). Counting we learned going up and downstairs, or sharing things out while we play. Shape, again easy during play to find or draw circles, squares, stars, triangles.
Having gone through this with two kids, I'd stick with useful words not faff around with reciting the alphabet sounds by rote at this age.