It’s a cliché in keto circles: “chase results, not ketones.” As others said, if you are only eating what you wrote, there’s no way you’re not in ketosis after a few days (barring some serious metabolic deficiency that prevents ketogenesis, in which case I assume you’d be either feeling horribly sick or dead).
If weight loss is your goal, the real question is are you losing weight? The problem with that question is that it is confounded by water weight fluctuations (which I suspect are sometimes overstated by people pooh-poohing keto, but there seems to be some truth to it) and so weight is something that presumably reads out reliably only over a time-course of weeks or longer. It would be reasonable to want a rapid form of feedback in ketone testing.
I am certainly guilty of testing myself. I bought pee sticks within a very few weeks of staring the diet. (They never showed much for me, except one day after a couple of months when I went sea-kayaking at a fairly good pace for almost five hours, then tested after that and after having not eaten for over six hours, but my spousal critter got visible low but positive test results under more “normal” circumstances.). I bought a Ketonix within the first year, although I later discovered that it is seems to be a false-positive generator, based on their own website. I’m now on my second Keto-Mojo, because they changed the design and I could no longer get test strips for the first one, and I just got a fresh box of strips last month.
I’m doing keto primarily for fear of dementia, not weight loss. I’m one of those hateful monsters who’s BMI seemingly CAN’T be not 21, regardless of my eating or physical training, so I wouldn’t know what was going on if I didn’t test. But testing for a love of data or seeing positive reinforcement is legitimate for anyone, IMHO. Just don’t assume that you have to hit a certain number to get what you want in terms of weight loss, from what I’ve read.