Mitchell Earl answered
Two simple tactics–that's it. You don't even have to get cute. Just prove you can do the job before you have the job.
First, go build a lead list. Figure out who DoorDash's customers are. Then go online and find potential new customers. Use resources like LinkedIn, AngelList, Crunchbase, Yelp. Then use tools like LeadIQ, ZoomInfo, and Hunter.io to scrape contact information for those potential customers. Then run the contact info through a validation software, like Kickbox or BriteVerify to make sure the emails are valid.
Then head to BuiltWith and plug in DoorDash's URL to get a list of any software integrations they have on their site. If there are any you're not familiar with, I recommend going to Udemy or Google (there are many great blogs out there on how to use almost anything) to give yourself a crash course in those tools. To succeed at sales ops, you need to be able to navigate most of the tools sales and marketing teams use. (And if you're not spreadsheet guru, I recommend taking Ben Collins' courses). For each software, I'd recommend writing a blog post or recording a quick video demonstrating your understanding of how to use it (and, bonus, demonstrate how you think DoorDash uses it).
Then, find the recruiter's email address from LinkedIn using the same tactics above. Shoot them a short email with the lead list and demos attached, and tell them you'd love to put your name in the hat for the open role.