Understand how to Identify return users to website within a week after visiting for the first time via a social media campaign

I wonder if something like a Cohort Table would make more sense... 

While I know you talk about the first instance... does it really make sense to look at first ever? Or just within recent times...  A Cohort would look at recency based on the actual entry to your site from Paid Social, then even if that user later came back via Organic Search, they would be counted in your returns.

If you have a specific Paid Social campaign, you could segment it to that specific campaign...

(HIT Level - Marketing Channel Detail "may-2023-special" for instance)

But looking just at "Paid Social":

You can use the metric "Marketing Channel Instance" and further segment it to "Marketing Channel - Paid Social" (I literally just expanded Marketing Channel and pulled "Paid Social" into the segment field, making a quick segment)

(If you have a specific campaign, then you could add that segment on top of this)

Then your return criteria would just be "Visits"

Set your granularity to week (or you could use "Day" and look at a week's worth of data - this would capture people returning with a day or two)

You can even "create a segment from cell" on your cohort and look at how it's built... 

Then you could actually modify this, to not look at locked dates based on the the cell of the cohort you used... but using some custom rolling date ranges... maybe in the first part look for a rolling "start" of 8 Days Ago:

and then in the second clause do a rolling return window of 1-7 Days Ago:

Hopefully this gets you closer to the data you are trying to pull