Know-How Exchange : Advertising/PR

Depending on the size of your mailing list, why not split test it? It may vary region-to-region so it's likely that there's not a universal best practice.

Also challenging is knowing when local utility bills arrive so as not to dilute your message.

From the UK:
https://www.bakergoodchild.co.uk/what-is-the-best-time-of-week-to-send-out-...

General:
https://www.smallbusinessbrief.com/forum/showthread.php?t=10911
https://www.themailshark.com/resources/blog/direct-mail-timing-tips/

Keep in mind, the day you send kind of sets the date it arrives. Assuming you are in US, if you send the full list at once, those close to your send location could get it a day or two earlier than those on the other side of the country (and crossing between mainland and Hawaii/Alaska could be very delayed).

On the list of decisions a direct mail marketer must make, I would think the drop-day is near the bottom. High on the list should be (1) target audience/list, (2) specific offer, and (3) positioning promise/core benefit.

Any of these would almost certainly outweigh the possible day-of-the-week variation.

FWIW, some/many marketers favor Tuesday delivery because it's the lightest day for regular mail delivery so they think the marketing mailing will stand out more. Not sure anyone really knows truth, and not clear that this applies everywhere or to every product category. Best way to decide (once you have the important stuff resolved) is with a split test as suggested by Jay Hamilton-Roth.