How do I create a infinite map?

My game is a simple iOS tap game where the characte must flip to the top or bottom of the screen to avoid objects that they are moving towards, it's pretty basic but I'm stuck on how I would create an 'infinite mode' where the map is randomly created as the screen moves toward it (I'm using flappy bird as an exampl because it's basically what the game is just a different idea aha) I've made the game so that the player moves toward the objects but would it be better if the objects rolled towards the player maybe? Any ideas?

Cheers

For endless type of map, I would prefer the player to stay in place and keep on spawning all obstacles and sending them to the player until the player is dead.

I highly recommend you move the objects, not the player.

Assuming the obstacles come from the right of the screen

1) Spawn obstacles off screen (right), set their X,Y and other values.

2) When the obstacles exits the screen on the left, change it's x,y etc and reposition off-screen right.

No need to create and destroy endless objects - reuse and reconfigure instead if possible.

I did this in my game Star Kite, that has endless levels too:

https://johnevelyn.itch.io/star-kite