What happens if a lot of applicants apply for the job after the company starts advertising? If the company has to stop the process since it might hard for them to make a case for me due to a lot of qualified applications, will it have negative impact on re-starting the process a few months later?

My company is willing to start the greencard process now, but i am in finance industry now where a lot of people laid off are seeking for a new opportunity. HR is kind of worried about not being able to make a case.