You have to understand the basic physics involved here.
NONE of these will EVER be able to actually crank an engine. Ever. What you are doing is attempting to TRANSFER energy to the battery, which then can source the current.
Assuming you have 12V/10,000 mAH (that's 10 AH.) Your battery is ~40AH. You can PERHAPS transfer 2/3rds of that 10 AH into the battery, or about 6 AH, which is ~15% of a full charge. This is simply due to the physics of things -- all transfer has loss and you're doing twice; once out of the battery pack and then again into your battery. You'll never get more than about 2/3rds of the "nameplate" rating on it -- and that's optimistic -- into the target battery from one of these. You MUST be certain EVERYTHING in the car is off while trying to do this because any consumption (e.g. dome lights, stereo, etc) will consume some of that power which would otherwise be transferred.
Why can't you just start the car? Because it takes a couple hundred amps or more to turn the starter and NONE of these, nor for that matter a set of standard jumper cables, can actually sink 200 or 400A! No way, no how, uh uh. The guys who drive wreckers may have a set of 00 (e.g. welding!) cables but even those can only sink a couple hundred amps continually -- YOUR 6, 4 or 2ga jumper cables cannot nor can that puny battery pack. (A 2ga cable is only rated for 100A continuous.)
A 20' jumper cable, 00 size, off a fully-charged source will be 10.75V at the other end with a 400A draw, assuming the clamps are not the limiting factor. THAT will start most cars but that little wire coming out of these packs and your common jumper cables will NOT. Even then if the battery in the dead vehicle has a shorted cell you're screwed as you will go under minimum cranking voltage. Now you know why the wreckers have those big beefy 00 or bigger ones in the truck. Oh, and not those Amazon ones either; those are junk; nearly all are actually copper-coated aluminum and neither the cable or the clamps are as advertised. You want real ones either spend a ton of money or go buy welding cable, clamps and make your own.
The other thing to be aware of is that all common car batteries are severely damaged or destroyed if drawn down by more than about 20%. If you draw it down far enough that it won't start, that is, it's mostly discharged, you HAVE sulfated the plates and the battery has permanently lost a good part of its capacity. There's nothing you can do about it. There's also decent odds it has an internal short in one or more cells, and if that happens then forget it since your "jump starter" will discharge itself into the short and fail to put the power where it needs to go (into storage in your car's battery.)
One final point -- Li chemistry packs like this really, really do not like to be stored fully charged. 80% is where you want them -- no more. That may or may not be enough. If you store them at 100% they will be seriously compromised inside of a year or two and will require replacement.
IMHO a decent set of jumper cables is a better investment; yes, you need someone else with a working car to use them, but they last forever in the trunk. They are subject to the same basic problem as are those packs however -- if you have a shorted cell it's almost-certain that "consumer style" jumper cables will fail to work for the exact same reason that the "rescue jumper pack" fails because jumper cables transfer power into the dead battery as again, there is no possible way you're sinking 300+ amps through them while attempting to crank.
