A child with one narrow obsession does not want a party with balloons and a licensed mascot. They want the thing they already love, taken seriously for one afternoon.
A three-year-old obsessed with dragons does not know or care which franchise your invitation was printed from. What they want is dragons — the idea, the shape, the roar — and that is free to build a party around. A licensed character costume or plate set adds cost and a logo neither of you chose.
Every party below is built the same way: take the thing itself, not a brand wrapped around it, and hand the child the closest real version of it you can manage for an afternoon.
A dig site, a volcano, and nothing to hire.
A sandpit, a hard hat, and a real machine if you can get one.
A cave, a hoard, and an egg hunt.
A cardboard rocket and a dark-room star hunt.
A blue tarp ocean and a fin hunt, no pool required.
Stable games, a hobby-horse race, and a real visit if you can get one.
The cheapest theme here, because the bugs are already outside.
No guests, no budget, still a whole themed day.