I’m not an expert here, but I did something similar in the summer of 2019. Collected some young branches of two different willows, grew them in a bottle of water for 6-8 weeks I believe. It took two weeks or so before the first roots started to appear. Once I had about 6-10 roots of 4cm or more I potted it up. Not that I think thats actually required because I think they grow roots in just about anything.
I made the mistake of using cheap potting soil because I did not have any proper bonsai soil at that time. It gave a decent result but thats just because Willows are such fierce growers. I probably could have done a lot better using a more aggregate soil like @Keith-in-UK and @CoffeeCherry suggested. After 1,5 years the soil was hard as a rock when slightly dry and very prone to rot when keeping it saturated. Not the way to go!
Just make it grow as much as you can now. Put it near a south facing window, give it some warmth and let it grow so it can produce roots as soon as possible. Once they take off, I shouldn’t worry too much. Now I worry more where I actually put them on because if you give them the chance to escape the pot, those roots quickly take over. Personally I prefer to keep them on the bench and force all growth in the pot (and consequently have to repot every year?) then cutting off all root growth that goes into a water tray or the ground.
Mind you, I did this at the end of summer, so to “let it grow” was a not that hard at that time.
I have some photos, not great ones but just to share my Do’s and Dont’s…
July 2019 - after 3 weeks of growth
I had put it in potting soil in and forgot about them in 2020. This is March 2021 after the soil became too bad. All surviving roots were on the outside and very little in the middle.
Despite the soil issues I had plenty of roots. But after 1,5 yrs this is not that much:
Trimmed down to this and then put in a mixture of 3 akadama / 1 pumice / 1 lava. I used more Akadama for the water holding capacity.
This year I’m going for 2 Akadama / 1 Lava. Lava also holds a decent amount of moisture (more than the pumice I get here in Europe) and it also doesn’t break down. Any other suggestions or ideas are highly welcome
Initially, after repotting, the soil level was below the edge of the pot. By September 1st, after roughly 5 months, it had started to push itself out of the pot.
I hope this helps. Best of luck and I wouldn’t worry too much!