You'll need to find a crafter. The most common way would be to use zone chat unless you know someone who can craft. If you're in a guild you could also try asking there. You could also try crafting for yourself, but it takes a bit of time before you can craft anything of note.
Which server are you on? If it's PS4 EU I could craft some for you.
Ah unlucky. I'd try to join a guild or ask in zone chat. If i see someone asking for training armor the low level zone chats I almost always will stop to make them one for free. I'm sure there are others like me on the EU server as well.
Zonechat is zone-wide so doesn't matter where in the zone you are. Try Deshaan, Grahtwood or Stormhaven zones, they're usually very lively due to Undaunted enclaves, so might find someone willing to help there. Reaper's March and Craglorn could also work if you have those.
You could also check out guild recruitment section to see if any new player-friendly guilds are recruiting on your platform, people are usually willing to help out in these.
I'm just starting out and in need of some training armour. Where can I purchase some?
go check guild traders. if you are in a guild (preferable a larger trading guild), go check the guild store. if you will not find it there, then ask in zonechat, or guild chat.
people usually require the materials to craft it for you. some require additional gold, but many craft for free if you provide the materials. if you do not have the necessary materials gathered, you can also buy them in guild trader or in guild store, for gold.
good luck!