If you had no connections, money, investments, or any property/possessions to sell, what would be your first steps?
Mowing lawns, gardening, shoveling snow, cleaning, odd jobs, etc... It does depend on your location but this is still a fairly common thing in some places. Knock on doors ask people if they need work. Point out things that they could use help with weeding trimming mowing all of that.
But if you take an average of $40 a job spreading that over 7 days that's 3.6 jobs a day. If you can do an average of 12 hours of work a day it'll be at your $1,000.
They pay better than most entry level jobs people gravitate to (fast food, retail, etc) and are nearly always hiring.
That'd a harsh set of constraints.
I think the only answers remaining with those in place are "prostitution" and "crime", aren't they?
Ditch a digit, $100 in a week, and you could do it with any normal job, stack shelves or whatever, but I don't see that getting you to $1k. $500 perhaps, from what I hear of US jobs (you did mean USD not any of the other dollars, right?), but not $1k.
https://alaskafishingjobs.com/earnings-and-wages/
https://www.goarmy.com/benefits/while-you-serve/money-pay (depending on how you count the various benefits, [re-]enlistment bonuses, etc.)