Google Sheets: Function which will return the closest row to a specific date for each customer in a database

I'm not sure if this is a pipedream, but I'm looking for a formula which I can insert into a sheet to pull the earliest and latest submission for each customer from a dataset. I have included a sample dataset.

Essentially, it will match the lowest date that is between two given dates. It will return the Submission and Date from All Submissions that has the closest date above H1 in that sheet and matches the Customer number in Column A in Earliest sheet.

I have been trying to use something along the lines of:

=INDEX(All Submissions!C:C, MATCH(1,(MIN(ABS(All Submissions!D:D-All Submissions!$H$1))*(A2=All Submissions!B:B)), 0),0)

Sorry if this makes no sense.

Thanks in advance.