If not dynamite, then something similar like a bomb from the DMG.
Both have a similar rules text:
As an action, a creature can light a [stick of dynamite/bomb] and throw it at a point up to 60 feet away. Each creature within 5 feet of that point must make a DC 12 Dexterity saving throw, taking 3d6 [bludgeoning/fire] damage on a failed save [./, or half as much damage on a successful one.]
Nothing there says it targets/counts as an attack.
The spell Sanctuary says:
If the warded creature makes an attack, casts a spell that affects an enemy, or deals damage to another creature, this spell ends.
Do the rules consider you having dealt damage once the explosive goes off? Is it any different if you set the dynamite to explode after a set number of rounds (assuming you are still under the effects of sanctuary), and perhaps an innocent bystander walk by while you aren't looking?
Best Answer
Yes you can...
But the spell ends when you deal damage with the bomb.
The rules don't specify this explicitly. But allowing indirect damage begins a slippery path of extreme rules lawyering ("this wasn't me dealing damage, but my spear"). In some cases, RAW falls short. The writers are only human and can miss details. That's why we need a DM, after all. A bomb-throwing cleric under the effect of Sanctuary clearly goes against both the intention and the spirit of the spell.
This is an edge case which needs DM's adjudication. I'd say it is still the character who deals damage. The character has agency, not the dynamite stick.