1. Easiest way to earn plat is to sell what people wants to buy.
I know this answer might not really satisfy you but... Whenever there is new content ppl are overpaying a LOT for single parts.
2. Its not hard at all to earn plat. When i started playing... which was a bit time ago, it was hard, but now? not rly. You go to warframe.market, check what thing is easily sellable and u just farm that particular spot to get this done. To increase the chance u go to :Recruiting channel, find ppl that have same relic as you do, and u farm them all in Radiant Share.
Lets say i launched the site, and searched a bit and i found "Volt Prime Neuroptics". Apparently they sell for like 60 plat. If u check where it drops u see Neo/Axi relics. So you basically progress through game, even on single, get to "Pluto", and select mission "Hieracon" in public. Then u just keep repeating that (leveling your frame as well) until u get desired (lets say) Axi V8.
Then u head to Recruiting and spam "LF [Axi V8 Relic] RadShare". After u find a party, all of you should have same relic upgraded on radiant and u just do it. Like 2-3 tries and you SHOULD get at least 1 part (+ tons of other stuff). Once u got tons of relics, u can simply spam these and u will earn your money eventually.
3. HOWEVER, when i played the game, i didnt have to invest platinum in either of my stuff. I just started farming. You DONT have to buy anything for plat, unless u want to look well.
P.s. Sorry for giving you tips how to make money but imho, u will have more fun and u will be more proud when u get to the point of 20+mastery all on your own