To stand out in the Local Map Pack, you are going to need to have a very well optimized profile. There are many articles, like this one https://coalitiontechnologies.com/blog/how-to-optimize-your-google-my-business-location, with tips on how to do that.
However, the Google My Business Profile mostly only helps you rank in the local area. If you have your physical store in New York, you can rank in the map pack for New York related queries, but not likely for other cities like Los Angeles.
Since you can deliver the products to other locations though, you could try utilizing the Service Areas feature to add in a list of cities the business serves. This may help to achieve what you are describing for some low competition search queries, however it doesn't guarantee that you will rank in the Local Map Pack for other cities since you don’t have a dedicated location there and more relevant and authoritative businesses in those cities will easily outrank you.
If it's not important necessarily what is ranking (organic search result or a map pack result), there is always the option to create several landing pages on the store’s website that are optimized for your desired local search terms (online clothing store in: los angeles, miami, atlanta, chicago, etc.)
Again, you’ll be competing with everyone else to get those top ranking positions, but that would be one way to try to get there. Good luck!
