Moisture decides where he went
A green tree frog's escape is a race against dry air, and that fact shapes the whole search. Unlike a snake, who can wait out a week in a wall void, a small tree frog loses moisture through his skin constantly, so he travels toward damp and then stays in it. Your search is therefore a map of your home's water: bathrooms first, then kitchens and laundry rooms, then houseplants, then anywhere a pet's water bowl or a dripping tap keeps the air humid.
Move faster than you would for a reptile, but just as gently — dry hands damage frog skin, so wet your hands with dechlorinated water before you touch anything you may need to lift him from.
Plants, pipes, and the bathroom circuit
Start behind and beneath the bathroom fixtures: behind the toilet tank, inside the cabinet under the sink among the pipes, along the cool rim of the tub, and behind any laundry hamper standing against the wall. Then go plant by plant through the house, turning leaves over one at a time, because a tree frog sleeps flattened against the underside of a leaf or wedged in the fork where leaf meets stem, colored almost exactly like the foliage he sits on.
Check window frames near plants, the damp soil of large potted specimens, and the folds of shower curtains. Shut each room's door as you clear it, and put a shallow dish of dechlorinated water on the floor of every cleared room: a frog who reaches it will stay near it, and a dish with a frog beside it at your next check ends the search kindly.
Listening in the dark
Green tree frogs are night animals, and the male's call is the loudest clue in this entire list of escapes. After dark, turn off televisions and running water, sit still in the hallway, and listen room by room. A frog calling from inside a plant pot or behind a bathroom cabinet sounds startlingly close and startlingly precise — walk toward it slowly with a dim flashlight and check the leaves and corners at that spot. Mist the plants in rooms you suspect; the rise in humidity encourages both movement and calling.
Water stations and the gentle scoop
If the first night passes without a find, widen the water stations, add a damp paper towel inside a small open container near each dish as a moisture refuge, and re-search the bathroom circuit at dawn, when he settles for the day. When you do find him, coax him onto a wet hand or into a ventilated tub lined with damp paper towel — never chase him across dry carpet, and never use tap water straight from the faucet on his skin if it carries chlorine; use the dechlorinated water you keep for his tank.
Back in the enclosure, check the lid and every seam, because a frog who can flatten against glass can pour himself through a gap you would swear is sealed. If he may instead have slipped out through a bathroom window to the porch or garden, search the plants out there at nightfall, and let nearby pet lovers know he is missing: KinsLe's Lost Pet Alert System alerts them for free, so a neighbor who finds a bright green frog on their porch rail can message you directly.