Automatically populate the Timeline Column with a Quarter's start and Finish Date

I am looking to use a Main Table to create a Company Roadmap. It looks like I therefore need to use the Timeline column to make the items appear on the roadmap view.

However, we operate in Qs and entering the Timeline for each Q is repetitive and there is room for error. Is there a automation / formula I could set up to get the timeline to populate with a Q start and end date?

e.g. if you created a Dropdown column with Target Q with Qs listed. If you selected 2022 Q4 in here it would automatically update the timeline column to 3rd Oct -30th Dec 2022 (taking working days into account for start and end ) . This would greatly help.