How to Extract a Period of a Periodic Pulsed Signal?
Natalia Molinero Mingorance, Welcome to the DSP community.

What you have is basically a shifted periodic signal.
Why? Because what you have is equivalent (Given many samples) of having a periodic signal which you started sampling at $ 0 $ and then we shit it to the real place you started sampling it.

Yea, there is the edge case, since it might not have  its end and beginning to make a complete cycle.

But let's assume our model is perfect, what would you see in Frequency Domain (DFT)?

Well, since shifting in time only changes the phase it means you won't see any difference.

So how would you extract the period of a signal you started sampling at the beginning of a period in the Frequency Domain?
Yep, just looking at the Frequency in the Frequency Domain.

If you post the files of the samples we'll be able to to see this together.