Order tiles now or only when needed?

Are you committed to a specific wholesaler for tiles or sanitary supplies for procurement? If yes, ask them if they can already order the material for you today and then store it on their premises; of course, you would pay the storage costs. This would have the advantage that they would handle logistics, timing, and warranty. The difference is that they would not order just-in-time as before, and you might have an extension of the construction time.

Otherwise, if you unpack the washbasin on the construction site after 12 months and it has a crack... then that would be your problem! So that’s from the plumbing/heating/ventilation (SHK) or their wholesaler. Otherwise, if the garage is right next door, I would also store the tiles there—we did it that way back then; the prefabricated garage was already in place during the shell construction.

Would you, as soon as the groundbreaking is there, immediately buy and have the tiles, floor coverings, fittings, etc. delivered?

I know it like this, that then the general contractor or his trade partner acts as the purchaser.

That was exactly my thought too.
Many here write, and it is true, that you have to take all the elements or even trades out of the contract in order to have the possibility of self-procurement (for whatever reason and whenever).
The house’s calculation is also based on wholesale prices and mixed calculation.
You as the client with the general contractor are in any case not contractually in the role of procuring materials.