There are some advantages to raised beds. It's an easier way to get the depth of loosened soil that double digging is going for and really helps with drainage etc. But it can be done without boxing it in.
Just lay out what are your beds and what are your paths. Now dig down your paths at least six inches, piling the dug out dirt from the path onto the beds (or in this case maybe raised wide rows).
Here's a little article about what I mean:
https://www.growingvegetablegardens.com/ ... _rows.html
Especially since your ground has been compacted, you do need to start by tilling, which is also the time to mix in all the compost and other organic materials. Then do the digging and piling on to the tilled ground. After it's all built, you may never have to till again.
Your raised wide rows can then be totally planted.
Note the article mentions having your soil tested. You really need to do this, to find out what you should be adding.
I know all this sounds like a lot of work, but you are laying the foundation for years of gardening. Your garden is only as good as your soil and there's really no way to cheat. You can't dump a bunch of Miracle-Gro on top of bad soil and think you've made it good, not the same at all.
Just for a little more quick reading, here's a thread where Scott, The Helpful Gardener himself, talks about raised rows.
https://www.helpfulgardener.com/forum/v ... hp?t=32655