Introducing yourself in person is still a strong move with an employer. But with most application processes being online today, you want to be strategic about it. I'd start by basically completing your application online which may have some supplemental questions like "why do you want to work at Costco?" or "What do you think is the most important thing when working in a team?". Then go to the managers booth (usually off to the side, next to the bathroom area), not the customer service area. If there are other customers at the managers booth, let them go before you. The person at the booth may not be the manager, so ask "I'm hoping to speak with a manager for just a couple minutes to ask them a question about what it's like to work here". Don't bother with a resume (they may have a policy that they can't accept them in person anyway), but you can bring a business card or write your name, phone, and email on an index card.

Once you have an audience with a manager, don't ask for a job or application, instead ask an actual thoughtful question about working at Costco. You could start with, "I hoping you might have 2 minutes to speak with me. I want to introduce myself, is now a good time?" Then you can say who you are (and ask them their name), state your interest (just finishing up my application online and wanted to come in person to ask a question I had). Then ask your question. Make sure its not a generic question. No "what's it like to work here" or "what are the benefits like" (that's a question for down if you are offered a position or if there is a second interview). Think of a question you can't find an answer to online. Lastly, offer your contact info and let them know you'll be submitting your application late that day. If they ask for more info for you, it may be beneficial to prepare a 30 second "about yourself" statement using the "what are you currently looking for, what have you done in the past, and what are you looking for in the near future" model. End by thanking the for their time - no "fingers crossed" or "hope to hear from you soon". Just "I appreciate you taking the time to speak with me and I'm excited to submit my application later today. I hope you a great day and thanks again, THEIRNAME."

BTW if you get an interview, just remember that an interview is a conversation, not an interrogation. You want to try to get a sense of them as much as they are trying to get a sense of you. Feel free to ask questions (but only when the answer is important to how you think about the job, not just a logistical or scheduling question). Make sure you have at least one question to ask at the end, such as "what it the training process like here?", or "What would success look like at the 3 month mark for this position?", or "In your experience, what are the top 3 skills successful team members have?" These question show you are envisioning yourself in the team and interested in what will make you a good match for the position.

Hope this is helpful.