Considering the ratio between necessary tutorials and unnecessary videos in your case, almost

.
You really should go through the basic in-game tutorials. Yes, also combat. There will be times, even in solo play, where you will be interdicted by an NPC. In
most of these case you will be fine if you're not carrying anything valuable, even if you don't do anything, but there's that one case in a thousand left which will let you lose all your earned, but unclaimed, exploration revenue.
Also, depending on what you understand as "exploring", you should at least know where you can find the in-game tutorials. Even (or especially) seasoned explorers tend to favour a short refresher course about how to land at a station over ramming a station wall or beating a hasty retreat (if they're lucky) because they forgot to request permission first.
If you're talking about Youtube - forget it. 90% of the stuff you can find there is outdated. If you want specific information (e.g. on how to get a specific upgrade for your ship), check (e.g.) here again and someone will most likely be able to point you at an actually useful and still valid video.
That said - going for exploration in your starter ship will be tedious. That ship is equipped with the bare minimum to get it out the door, but not much farther. Especially considering that it doesn't even have a fuel scoop, so unless you remedy that, you are forced to dock at a station for refuelling (and now we already have covered something like 5 of the in-game tutorials: taking off, flying, jumping to another system, landing and interacting with the station).
The seemingly bad news is that you will need around 10 MCr. for a nice exploration ship (Dolphin). The good news is that it's easy to make that money.
The worse news is that, in order to unlock the full potential of this (or any, for that matter) ship, you'll need to start messing about with the Engineers (btw., I hope you got Horizons - exploration without planetary landings is going to be pretty boring). The good news in this case is that, by the time you have unlocked the basic Engineers, you can also afford almost any any ship - at least any ship worthwhile using for Exploration. Ok, maybe not the Anaconda, but that's a barely flying brick in any case.
Ships and upgrades - once you manage to get your Sidewinder out of one and back into another station, it might be worth checking out ship configuration sites like
Coriolis, to see what options you have with ships and their configuration.
Inara can give you a good overview of the Engineers (if you don't prefer to learn about them step by step inside the game).
EDDB and
EDSM can give you the details about what's out there, what you can get where, what you can sell where etc. If you play on PC,
EDMC and
EDDiscovery can read your CMDR logfiles and use them to automatically update EDDB or your EDSM profile - or record and show on your PC where you've been and what you did there (and why you died).
Or you can just dive in and explore everything by yourself, through trial and error. Blaze your own trail, CMDR - and have fun.
P.S.: By "going through" inthe second paragraph I didn't mean "succeed" or "beat". Especially the advanced combat scenarios are advanced, and you'll need a bit of experience (or a detailed script) if you want to beat them. But you don't lose anything by losing there, either.