There is free DLC for this title on the Microsoft Store that gives you a whole bunch of Synth recipes and the items for those recipes
The DLC needs to be 'unpacked'. You can do this by pressing Y to open the menu and scrolling across to items. From here, scroll to the wifi/network looking symbol where you will find them
By utilising this DLC in this manner, you can synth at the very first store of the game. This has a number of advantages; earlier-than-usual achievement unlocks, stronger equipment much earlier and passive skill acquisition at an earlier point and a faster rate (by prioritising the items with the 'Happiness' skillsets)