Compare a beast mode to an arbitrary date range

I've been asked to create a trend that shows the number of open projects (y-axis) for an arbitrary date range(x-axis). A sample of my data looks like this:

The users want to be able to choose a date range, say 4/1/2024 to 4/7/2024, and see how many projects were open for each date interval in the range they selected (trending). The data above would yield a result like this:

I'm struggling to create an x-axis of dates independent of dates in my data that I can use in a beast mode to compare to open & closed dates. Is there a way to do this without building it in the ETL? Currently I use a couple variables for custom date ranges, but I've never had to create a range where the dates in my data are not the relevant axis. I'm trying to avoid adding a count by date in my dataset because there are several other metrics I'll need to group by which will result in a large dataset only used for this card.

Thanks for any advice!