We had around maybe 4-ish street hires in my class last month. I didn't get a chance to ask everyone what kind of stuff they had in thier application package, but one guy I know was a check airman at his regional, and had a few letters of rec. Who those letters are from seems to hold some weight, for example, AA senior CA's, chief pilots, ect. Another street hire came from a major cargo company. A few folks that got hired from my former regional as street hires, were either check airman and / or had worked in recruiting, or family member of senior AA pilots.
So if you don't meet any if the above, get involved in extra activity within your airline; ie check airman, training dep, CPO, safety dep, ect. And network like crazy to get heavy weighted LOR's.