There is a 12 tooth cog for a 7 speed freewheel but this falls into the category of hen's teeth... I have one on a Suntour freewheel that I built up custom for my folder and only had one 12 tooth cog among hundreds of other cogs to use.



13-x freewheels also tend to be at the higher end of things and can also be pricier.

Best option is to see if larger chainrings can be installed to up the gearing or to purchase a new wheel with a cassette hub that will take an 11-x... modern hubs are spaced for 8-10 speed cassettes so running a 7 speed cassette requires the use of a spacer.

Also... the gearing on the mtb should be high enough for some good speed and the easiest way to go faster is to learn how to spin faster and more smoothly and not by trying to mash a larger gear.