The statistics for employees from feeder companies like Goldman Sachs getting into an MBA program are much higher when compared to a small organization. However, business schools have repeatedly said and we have personally experienced, the quality of work experience over the name of your organization wins every time.
Skill sets like leadership, team-work, interpersonal skills, are cliché and over-used but they definitely add up when applying to a business school.
As per the additional information you have provided, missing a feeder company on your resume might not be something you should be concerned with. Also, having a feeder company on your profile does give you some benefit while applying to business schools, but missing the same doesn’t make a world of difference.
Just to cover all the bases, there are schools that have higher acceptance for applicants from feeder companies. In 2019, Stanford GSB enrolled over 120 students that came from feeders like McKinsey, Bain, E&Y, etc.