How should i go about transplanting into new soil.

Hiya there
So i'm about 2 weeks into my grow, i have 2 greenomatic autoflowers, now by this stage they should have some decent growth, but i just have the first 2 leaves only about 1cm long, and the 3rd and 4th leaves have just appeared.
Now, i've concluded that the slow growth is due to my terrible soil, it was cheap to start of with, but its been laying around in its bag for a good year or so exposed to rain, sun and whatnot.

So i've bought a new bag of potting mix, and might even try find some perlite, but my question is, how do i get this seedling into the new soil. All that i've been able to find is how to transplant when root bound, but i want to completely get rid of this soil, and utilize the new soil. How do i do this?

i would say remove the plant from the current pot, lightly hose the root system and remaining old soil off or maybe move into a bigger pot n sorta try crumble n hose off

talk about slow growth after ya transplant. prolly bonsai it for a month if not possible kill it. I would just put the new potting soil on the bottom and repot into a larger container.