The answer is yes, absolutelyvne enough time. You can do this experiment yourself. Get a clean glass jar, hell even sterilize if if you like (your oven overnight at 250 F will do it). Fill it about 3/4 with clean (or even sterilized) water, and leave it outside in a mixed sunny shady spot for a few weeks, in moderate weather. It's small volume will get cooked by constant direct sun, which will impede the results.
After a few weeks (might be faster), look closely into the water (through the sides of the jar) with a magnifying glass, or better still, sample the water and look under a microscope. You won't see, but they are there, multiple bacterial species.
You will see single celled algae, small pond creatures (hydra, rotary-topped species (multiple)), paramecia, and multi-celled algal forms in strings. These are all fallen in from airborne dust and windblown particles. You likely won't get fish, but if you are lucky, you might get a few brine shrimp. And yes, particles of blown or bird-carried dirt etc can easily carry shrimp, amphibian, or plausibly, viable fish eggs.
But what do they feed on? There's no food in the water you put in !! CO2, nitrogen, Oxygen, etc are readily available from the air. A few cells of bacteria or algal forms seed the clean water, and begin fixing CO2, nitrogen etc, and now you have a food source. Wind-carried (or bird-carried) small organisms can now survive in a web of bacteria-plant-animal interactions.
By the way, you can also run a control jar, where you sterilize the jar, fill it with boiling hot water, and quickly cover it tightly with foil. Place it beside your open jar, and it will grow...nothing.
As a side note, "toxic" algae are often not toxic to small organisms and other algae. Their toxins (neurotoxins usually) affect mostly only higher organisms, such as fish and humans. Algal blooms kill fish and birds, they seldom sterilize the pond.