As far as sponsorship acquisition goes, James’ post is pretty spot on. This is karting, sponsors are verrrrrry few and far between.
Regarding your goal of eventually racing open-wheel cars; there’s no need to be in a rush. I assume you’re racing because you love it. There are plenty of drivers who are older than you and still are getting chances in the open-wheel ladder. But not just off of one or two good national finishes. The best drivers in karting right now, the guys winning the biggest events every weekend still need a big check before anyone is going to offer them a car to drive.
The worst thing you could do for yourself would be to rush forward and move up to something you’re not ready for, and hurt your development as a driver. If you don’t have time or money to travel to national karting races I’m not sure how you are expecting to get through the open-wheel ladder, where you’ll have to dedicate ALL of your time and money to buying rides as you go up the ladder. From a sponsor’s perspective, what benefit do they have from funding a junior open-wheel driver that isn’t getting any exposure from media or fans?
I don’t want to be the rain on your parade, but keep in mind that there are 20-30 IndyCar drivers and 20-30 F1/reserve drivers who are actually making a living in open-wheel racing, in the world. The odds of getting there are very low. Like insanely low. To make it, you need a ton of money, and you need to be the best of the best consistently over many years. There’s really no way to rush up the ladder or take any shortcuts. It’s going to be hard work, a huge cash investment, and constant winning.
It’s good to have goals, so keep working toward those. My advice would be to continue karting for now until you’re a consistent front runner at events like Pro Tour or USPKS, and that’s when you need to start to worry about how to progress. Up until you get there, unfortunately it’s pretty much going to be on your own, as the funding available from potential sponsors is almost zero unless you have some unique perk or benefit you can offer someone. Everyday I see good drivers that I’ve personally worked with to coach and train, with unlimited money, try and move up and they can’t make it.
Keep racing, because it’s fun and you love it, and don’t rush it.