You're first mistake is sending applications. If you're applying for a job, than you're competing with a bunch of other idiots. The jobs you want are the jobs no one applies for.
Please put yourself in the shoes of a company owner. You receive a job application from individual A, and individual B comes in and tells you that he loves your company, and describes some great ideas in which he would like to help you improve your company, and make it even better, and would like to write you a proposal. Who are you going to hire? The idiot who expects to be told what to do, or the go-getter who literally just wants you to unleash them on your company?
Big corporations are ran by policy. This is because policy is the only way executives can manage managers. Managers of large corporations such as the ones you've described are not very smart. Their job is to follow policy by the T, and make sure the laborers do their jobs. The laborers are at the bottom of the food chain. They have jobs which are very repetitive, and require a small amount of thinking.
In American society, you have the following Castes:
Owners
Executives
Engineers
Managers
Laborers
If you are an owner, you're job is to get great executives with ambition.
Executives will have the ability to get things done. They will be self directed. No one really tells them what to do. They know what needs to be done. They wake up on their own, and they are motivated not by Money, but by the cause they have committed themselves. This could be their project, the company, etc. These executives are the people who care the most. Most executives have very high level degrees. Why? Not because they are smarter, but because they are willing to put up with a LOT of crap to achieve their goals. This is the level of dedication and ambition you need to be an executive in this world, and sadly, 90% of Humanity is not genetically or mentally capable of being a successful executive.
Engineers solve problems. They create. They are the genius of the corporate world. They might not be good with people, they might not be good managing themselves, they might not have ambition, but they have skill, and executives pay well for it.
Managers are your "enlisted non-commissioned officer" level of Human society. You get a bit of a title, but you're payed nothing, you're a minion of an executive, and your job is to follow policy, and make sure everyone else follows it to. Most people who are managers in this world.. are not very ambitious I'd say. They don't make much, and they don't have much say in corporate affairs. They are kinda jokes to me, but they live an easy life I guess.
You're labors are young people, and people who have no self confidence, or perhaps no ambition.
Any laborer can easily turn into an owner.
Step1: Pick a fun service you would like to provide for businesses.
Step2: Find businesses who will benefit from your service
Step3: Ask the business if they would be interested in a proposal
Step4: Write amazing proposal that shows your dedication, skill, and an amazing plan that will improve their company.
Step4: Show up on time, communicate with them effectively, make them feel important, complete your objectives, and invoice them.
Step5: Expand your client base until you have no personal time left, than begin to raise your prices.
Step6: Hire a minion, and start selling their time. Grats, you started a company, and expanded!