You don’t need a quality seed bed. If you have access to an ATV with a sprayer, that is all you need. Even Rye Grass needs good seed/soil contact.
Assuming there is grass growing in that opening right now, odds are it has well established root and would take a lot of work to turn over. Here are my suggestions depending on the equipment you have access to.
First, if you can just cut the grass in August and fertilze heavily that is much better than the way it is right now.
If you have and ATV/Sprayer, cut the grass at the end of May and then burn it down with Roundup a week after cuttting. In mid July, come back and burn it down again with Round-up. You should now have all the cool and warm season grasses killed as long as you don’t underspray.
A week after spraying, go in and plant a perannual Rye grass. Since you don’t have equipment you will need to broadcast the seed. You want to broadcast it at a rate twice what you would drill. Rye is cheap so buy and extra bushel.
In mid August go back in and fertilize with 10-10-10 (it is cheap) You are now set until next spring.
The following spring you want to find something to work that Rye under. It is good for the soil and will work as fertilizer for you that year. If you get after in in spring you should be able to keep the weeds out. Round-up makes up for a lot of equipment, as weeds are the biggest issue with most food plots.
Getting a good food plot takes time. It may take you a few years to get after the weeds but you will win with a little work and effort.