So like 4/4 time is really telling you that a measure is 4 beats and each beat is a quarter note.

If you only wanted two beats you would call it 2/4 for one measure. You can't play part of a measure and start a new measure there that I've seen.

Good to put your specs in your signature, click below in my signature.

In other words: the signature sets the number of beats in a bar, but it doesn't change the tempo. To change the tempo you want to change the beats per second value in the tempo bar, and tempo changes can be anywhere in the bar

Tempo was never mentioned in the OP. Tempo is also measured as beats per minute BPM

There is no need to change the signature at say 26.2 though. That is the same as making the pervious bar eg bar 25 (beat 1) a 5/4 bar. Then on bar 26 (beat 1) you could change the signature again to something different.

Even if you wanted a time signature change on the third 1/8th note of bar 26 you can still do it by either making bar 25 an 11/8 bar on beat 1 or make bar 26 a 3/8 bar.

I do this all the time with film scoring in order to meet hit points much easier.

Jemusic wroteTempo is also measured as beats per minute BPM

Already felt a bit odd when I typed that

And yeah, to move the downbeat you have to change the time signature of the bar before it.