It's supposed to be part of the puzzle.

Here's a hint if you want one: As far as I know, it is not possible to do anything in the beginning other than arrive at the target host at an unknown cycle. What could possibly be affected by the cycle count? It's a mechanic/quirk that is quite easy to accidentally ignore.

...which unintuitive mechanic?

It is possible. It says "POWERED BY UNINTUITIVE MECHANICS" for a reason.

Without a second and third EXA, how do you determine both the test run's cycle number AND the timestamp that the link opens up? An EXA on its own can't count to itself.
If two of the nogo registers at home is removed, i can devise of a simple way to determine #WAIT:

XA does link 800, link 800, copy 1 M
XB counts to itself with a file
XC kills XB when TEST MRD is true and grabs its file, and outputs it to GOAL (wiping its file and killing XA)

to garret: It is possible to determine between 0 and 1 by a quirk of the timegate: 0 actually means one cycle before opening, and 1 means two. So if you do link 800 twice, you will get through 0 immediately. But for 1, you will pause for one cycle. So determining 0 and 1 isn't a problem

It does still seem impossible due to size constraints before TARGET is available...

Are you sure this is possible?
I mean - even if there was room to spawn anything, how could I determine between 0 and 1 for example ? Presumably I'm just too stupid, but have you actually solved it yourself ?