Let's see: A 2 gal tank. No heater and you live in Canada...
I would grow somewhat slow growing low light plants that could make it in somewhat cold (say 72F) aquariums as Anubias barteri var. nana or var. petite and Vesicularia dubyana (Java moss) placed in one or two tiny sized driftwoods and Cryptocoryne walkeri var. lutea at the foreground or all around the tank, aiming at keeping two Nerite Snails and a trio of Ghost Shrimp.
Of course I would keep plants only while cycling without inverts.
For filtration, a small sponge filter will suffice. Using 3" deep substrate (e.g. a mixture of Eco-complete or alike with sand) with some cobblestones here and there...
It is doable and might end up being an interesting set-up.
I managed to keep a Pistia stratiotes (Water Lettuce) and it adapted by growing way small and developing almost perfect circular shaped leaves while placed just underneath a 7W incandescent bulb in a similar tank as yours (mine was manufactured by ToM) and a couple of short stems of free floating Ceratophyllum demersum (Hornwort). These plants require moderate to bright light but they made it. I kept a juvenile Pla Kat
betta male for a couple of months, then left inverts only. Actually I use that tank for green water (Infusoria).
I have another like it as emergency tank for small fish and fry that require short isolation or medicated baths.
Pepetj
Santo Domingo