Matching just the first and second block of an URL - regex

Question

I'm trying to do a regex to match just the second part of a URL and leave the rest behind
For example
https://example.com/first-part/second-part/third-part/?prop=2
result = https://example.com/alt/second-part/
How can I do this?
I'm able to match the first two parts but for when I use the "/" for match it picks the last / one, instead the one before.
I can go the simple way like this:
RewriteRule ^(.*)first-part\/(.+)\/(.*)\/(.*)$ https://example.com/alt/$2 [R=301,L]
The problem is that if the URL is like this:
https://example.com/first-part/second-part/
Result expected. https://example.com/alt/second-part/
It won't even match it
So I'm looking for a more generic alternative, that may match multiple scenarios giving the same result ultimately in the same format:
https://example.com/alt/second-part/
Just knowing how the first-part exactly is and not knowing how anything beyond the second-part will be formated.

Answer 1

Taking into account the recommendations of #Eraklon to avoid the greedy checks I've found out a solution:
RewriteRule ^first-part\/([^\/]+(\/)?)(.*) https://example.com/alt/$1 [R=301,L]
Can be checked here:
https://htaccess.madewithlove.be?share=8973fe68-f137-59a5-b27b-0cbbe3d842bc
It exactly matches the first-part with ^first-part/ and then in enters the group:
([^\/]+(\/)?)
That checks for 1 or more chars that are not a slash /. When it finds the first slash it can be the next section of the URL or the end of the URL.
Not sure if this is the best but the idea is that it matches just 1 pattern for $1 that includes both the end slash and not-slash for the second-part block of the URL.
I've not been able to remove the last bit from the url (the parameters ?parameter=a)
So the result with this form a URL like:
https://example.com/first-part/second-part/third-part/?parameter=a
Will be
https://example.com/alt/second-part/?parameter=a
Fortunately, the parameters are not too bad, but I would have preferred the full solution.