he very first Antimatter in the game will be given to you for free in the starting star system. The warp cell you make from it gives your hyperdrive just enough power to warp to your second star system. And from this point on you'll have to craft more warp cells yourself to progress further in the game. Fortunately, you will once be guided via a beacon signal to the alien carries the Antimatter Blueprint. Go pick that up and you should at least know what's necessary to craft the all-important item.
Now to make an Antimatter, the recipe says you need an Electron Vapor, 50 units of Heridium and 20 units of Zinc. Again, the Electron Vapor can be purchased from galactic trade terminals or be manually crafted based on the recipe you already have on hand. To make an Electron Vapor, you need 100 units of Plutonium (can be mined from deposits on planets) and one Suspension Fluid. You can buy the fluid from trade terminals as always or craft it yourself should you manage to locate the recipe for it.
Back to the Antimatter, the remaining two ingredients (Heridium and Zinc) can be gathered with the mining tool while exploring planets. For the most part, Heridium is quite a bit harder to come by than Zinc and can be mined only from large blue slabs of rock. Zinc on the other hand is much more common and found from plants and flowers.
Once you have all the necessary pieces to craft warp cells at will, there is really nothing to keep you from exploring the vast (albeit same-y) universe of No Man's Sky assuming it manages to hold your interest long enough. In addition you will eventually get your hands on a blueprint for the Warp Reactor which will make warp jumps even easier. Although you can also find new starships that have warp reactors already in place.