Not to step on any other answers which are hopefully coming, but you might check out this answer by u/Holokyn-Kolokyn to start with.

Here's a previous answer of mine: https://www.reddit.com/r/AskHistorians/comments/iueqwb/why_did_it_take_so_long_for_the_bicycle_to_be/g5qk4pp/

To summarize, bicycles rely on essentially a small handful of core inventions: chain driven drives linking two gears, bearings, and metal frames. Other aspects are also highly desirable and contributed greatly to the widespread adoption of the bicycle, especially rubber (or even better pneumatic) tires and wire spoked rimmed wheels.

You can build a "sort of bicycle" without these things but it won't work very well, won't last very long, and will be a terrible riding experience. As, indeed, the very first proto-bicycles proved to be.

All of the things above more or less require a level of industrialization to pull off which wasn't prevalent until the mid 19th century when iron/steel production became ubiquitous along with advanced machinery.

In principle, if you had infinite resources you could time travel back to, oh, say the early iron age or even the bronze age and have a bicycle and all of its components built using handiwork, but it would be extravagantly expensive (like, wonder of the world expensive).