How can I increase the damage of my cantrips?

Question

Dangerous Sorcery does not work:

When you Cast a Spell from your spell slots, if the spell deals damage and doesn’t have a duration, you gain a status bonus to that spell’s damage equal to the spell’s level.

Neither do Sorcerer’s Blood Magic:

Whenever you cast a bloodline spell using Focus Points or a granted spell from your bloodline using a spell slot, you gain a blood magic effectfect.

Burn It! does not have this condition:

Your spells and alchemical items that deal fire damage gain a status bonus to damage equal to half the spell's level or one-quarter the item's level (minimum 1).

How can I increase the damage of non-fire cantrips?

Answer 1

The obvious and primary mechanism of increasing Cantrip damage is gaining levels, and increasing your casting modifier (for those cantrips to which your casting modifier applies). All Cantrips automatically heighten to the highest spell level you can cast. Thus, for example, Produce Flame, which does 1d4+Casting Mod damage at level 1, will, for a level 7 caster, be a level 4 cantrip, and do 4d4+casting Mod. As you've noted, feats that broadly increase elemental damage, such as Burn It! will work too.

If you're playing with, or are a Bard, don't forget about the effects of Inspire Courage and the boosts to that which are available, which affect your Cantrips as well as the attacks of your martial companions. In fact, it's doubly effective with multi-target cantrips like Electric Arc.

Another option is Metamagic; while there are no direct damage increases, you could, for example, use the Forcible Energy Feat, as a wizard, to impose weakness to a cantrip's damage type in one round, and then use the cantrip again to deal damage of that type in the next round with a bonus. If the target is resistant to the damage dealt by your cantrips, you can bypass some of that with Overwhelming Energy which is functionally a damage boost, though you'll usually be better served by simply casting a different cantrip.

The Eldritch Archer dedication will let you tack your cantrip damage on to a weapon attack, in much the same manner as a spellstriking Magus, dealing the full damage of both. With appropriate weapon runes, this will often roughly double your damage.

Also for an Eldritch Archer, or a Magus, or other weapon damage dealing caster, there is also the option of Spellhearts. A new category of magic item added in Secrets of Magic, Spellhearts function sort of like Talismans; you attach them to your weapon or armor, and they provide a bonus affect associated with those spells. The Flaming Star, Grim Sandglass, and Trinity Geode all provide bonus damage for a round on weapon attacks, following the casting of a cantrip of the linked element.

Answer 2

I've been looking at the new Psychic class which is included in the Dark Archives Playtest and it would seem that a good portion of their kit is cantrip based, with a unique ability to "amp" certain cantrips. You might keep an eye out for this if your question is more general than class-specific. The "downside" is that you are relegated the Occult tradition, which has comparatively meager options for damage cantrips.

Edit: Since the selection of cantrips able to be amp'd is rather narrow and the ability to amp is based solely off of action economy, my answer is extremely situational and doesn't entirely answer the OP's question.