Maksym,
A lot of negative vibes here..Pay attention to them, but don't let them put you and your ideas down.
Me and my buddy did it. Got our whole trip sponsored. Cycling from Alaska to Argentina on bamboo bicycles to raise awareness for the global water crisis.
The trick is, you have to be original and have a convincing and passionate story to tell. And, very important, make it clear to your potential sponsors in what way you are giving them value for their sponsorship.
Initially, we got a whole bunch of negative replies from sponsorships requests whole working on our project. But, we didn't stop or changed our strategy. At some point we found a big corporation that could identify their business, goals and ethics to ours, and a partnership was made. You need to invest heavily in your own project first though, before you try to get somebody else involved. This can be time, money, blood, sweat, tears. Preferably all of them, hehe!
Once on big corp gives you a 'stamp of approval', it becomes easier to get others involved.
Anyway, good luck bro. You can always msg me for more info!