Unless it rains, I can almost guarantee you will NOT get front street parking without a tag numbered between 1-250.
It's been very rare and generally causes quite a ruckus if anyone gets First Street parking that does not have a tag number 1-250 even though they may have room at the end of the street (I've seen them move people and people leave in a huff because they wouldn't let them park on First even though there were visible spots).
The problem is that competition for spots is tight all around (Especially on nice sunny days). Tons of pre-registered cars, including those with numbers 1-250, start lining up as early as 5:30am (Rules says not to line up before 6:00am but people will be there).
Those who line up early with numbers above 250 are there to snag spots on the feeder streets closest to First, so once they’ve parked, they get really torqued, if some yahoo rolls in and gets to park where they couldn’t, especially those who may have been forced to park at the top of a feeder street.
If First street is important to you, my only advise is to arrive early to snag a corner spot, or register the day your notice arrives in the mail and hope you get in early enough. Or Purchase/Trade with someone who has a number between 1-250