You can find cigarette-type USB3 plugs that will give you 3A, but I think that is it since that is the limit of the USB3 spec. You’ll have to see what the SSD draw is–some are a lot more than others–to see if you can live within 3A.
You can also find cigarette-type PD versions that will go up to 30 watts, but only 2.4A at 5v. Those would be worse for you.