If you keep your character exactly where they are (don't progress any further in the tutorial/story, and certainly don't go past the part where you'd get said transponder), you can resume during the next recruitment event and get the transponder on the character later.
I did this with the temporal recruitment.
I had a character I forgot to progress to the 25th century, so I let them sit at level 8 or so for 5 years until the next recruitment started.
Then I just loaded them up, continued with the story, and got the transponder once I hit the 25th century.
I wanted to post this here since I've seen various comments and posts on Reddit without this information (and I don't have an account there).
Here's my Captain's log showing the dates:
LTS Since Beta (Jan 2010).
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