Step by step tutorial on verifying blockchains

Hello, I would like to try out solo mining XMR but am running into an issue downloading the blockchain using their official gui wallet application.

I believe that this is due to a lack of P sharing it on their P2P but could be wrong about that. All I know is I have been tryibg to sync appropriately 60 gigs for more than 2 weeks.

It seems that there are 3rd party "cloud" based services that allow you to make teansactions using their remotely hosted blockchains but this seems like an even greater vulnerability than a 51% attack.

Is tbere a tutorial on how to validate a blockchain if downloaded from a 3rd party? Something like a crc check?

I will probably let the gui keep doing it's thing for XMR but plan on dipping my toes in ETH and BTC but would like a faster process if possible.

I hope what I am asking makes sense, thank you.