How deep should I dig the hole for a mailbox post?

2 and a 1/2 3' down

These will help you.

https://www.homedepot.com/c/ah/how-to-install-a-mailbox/9ba683603be9fa5395fab90b2bec3c6

https://www.wikihow.com/Install-a-Mailbox-Post

Hello, I would definitely suggest using a post hole digger. They are efficient to dig a small but deep hole for the mounting post. The recommendations specs are as follows

USPS requirements state that a mailbox can be no taller than 45 inches above street level. Since most streets have a curb, the standard mailbox height is 42 inches above ground level. So the total height is around 45 inches: 42 inches from the ground, plus the few inches added by the curb.

• Measure the height of your mailbox post. USPS requirements state that a mailbox height must be 41 to 45 inches above the road's surface. Standard mailbox height above the ground is 42 inches.
• Mark a spot on your lawn six to eight inches back from your curb. If you do not have a raised curb, contact your local postmaster for guidance.
• Use a post hole digger to dig a hole for your post at this spot. Dig deep enough that the height of your mailbox above the ground is around 42 inches. Do not dig deeper than 24 inches. Hope this helps.

it is a question of leverage the mail box will be subject to. If minimal then a post hole auger will suffice but beware of anyone leaning on it because it is in a soft substrata.