It is easy to be strictly vegan, as commercial "chemical" fertilizers and pesticides are all vegan. If you want to be vegan, and you also want to be strictly organic, then you are very limited in what commercial products you can use as so many of them contain animal matter, or simply are not labeled with what they contain. There is natually mined sodium nitrate, which is close to 100% sodium nitrate and no different than "non-organic" sodium nitrate made from Haber-process ammonia. However such naturally mined sodium nitrate costs much more and you may not be able to get it locally in small quantities. So to be vegan and "organic" ("veganic") you have to make your own compost and use cover crops and green manures. If you want to be sustainable, you don't have to be strictly organic. But then there is no commercial product you can use whatsoever. The idea of sustainable is that there is no input from outside. So you are back to compost green manures and cover crops, but you can't buy anything to compost, you must collect it from your own land. If you want to be strictly vegan but are not concerned about being strictly organic ("veganic") or strictly sustainable, but want to move in that direction, then you can use as much compost and green manures and cover crops as you can, plus any nitrate or ammoniacal commercial product, or commercial urea - all made from haber process ammonia. Plus phosphates and potassium are widely available in "natural" form or processed form (which don't meet regulations for being "organic;" they are naturally mined minerals which have been chemically treated to make them weigh less, and be cheaper to ship. The act of chemically treating them makes them not "organic." Haber process ammonia while not acceptable for "organic" or sustainable, is vegan. As far as pesticides go, commercial pesticides are all vegan, but some are "organic" and others are not.
To make compost in huge quantities, you can use tree leaves. You can collect the leaves that people rake up, and compost them, along with small amounts of vegan food scraps. If you live near the sea you can collect seaweed. You have to limit quantities due to its sodium chloride content. Some plants can tolerate more NaCl than others. To be strictly sustainable you can't even buy seeds because them come from outside. But as a practical matter, they contribute only a tiny percent to the total mass of materials involved.
Haber process ammonia while not "organic" is made from aerial nitrogen combined with the hydrogen from natural gas (or coal or petroleum) at high temperature, in the presence of a catalyst such as ozmium. It is vegan.
Tree leaves tree leaves tree leaves. I would suggest composting as many as possible. To an extent, you can also work them into the soil directly. Trees bring up minerals from the subsoil, which plants with shallower roots cannot reach.