While I was rolling to attack for my Warlock's Eldritch Blast, I said I don't think it gets my Spell Attack Bonus because I didn't see it say such anywhere, and the DM (also new to D&D) agreed, said it sounded correct as cantrips don't get the bonus. As I have been reading however it seems that they do get the bonus to attack rolls, it just certainly doesn't carry over to damage save rare exceptions. Can anyone verify this to me? And if so, show a source so I could let my DM know?
Yes, Cantrips get a bonus to attack.
From page 205 in the PHB we have that all spells benefit:
Some spells require the caster to make an attack roll to determine whether the spell effect hits the intended target. Your attack bonus with a spell attack equals your spellcasting ability modifier + your proficiency bonus.
And from page 201 in the PHB we can see that cantrips are considered spells:
Every spell has a level from 0 to 9. A spell’s level is a general indicator of how powerful it is, with the lowly (but still impressive) magic missile at 1st level and the earth-shaking wish at 9th. Cantrips—simple but powerful spells that characters can cast almost by rote — are level 0.
You are correct that there is no mention of all spells getting a bonus to damage based on your proficency or your spellcasting ability.
Yes, cantrips do benefit from spell attack modifiers - d20 + Proficiency Bonus + Spellcasting stat modifier; but this bonus is only for the attack roll.
Cantrips are treated as any other spells; just think of them like 0-level spells.
You can add modifier to damage only if a spell, or certain effect description, says so - for example, the Agonizing Blast invocation adds your Charisma mod to any Eldritch Blast attack that scores a hit.