I don't think you should worry. Even I worked in startups and even in proprietorship companies. Even for the biggest companies, they look only for genuine talent and experience. It doesn't matter whether you are from MNC or startup.
Only thing you should worry is about your scope of work and how you develop your talent. To achieve your goal to work in a target MNC company, develop your skills inside your current company and personally.
As documentation part, make sure that you have Appointment Order, Review Letters, Payslips, Bank Credit Statements, Experience Letter and Relieving Letter.
9th August 2017 From India, Chennai