What is considered new grad or entry level across the industry is bizarre. If the responsibility level and compensation matches your desired role, I don’t see any reason not to do it. I know that some places cap this at 1 year from graduation, or 1 year of professional experience or whatever, but not all do.
Not all experience is equal, either. The growth I had in the 8 years I was at Amazon was significantly different than the growth I had the prior 8 years I had worked in industry.
I don’t think there should be shame or guilt associated with taking a recent graduate role unless you’ve been promoted to intermediate roles elsewhere and it’s actually a step back in terms of responsibility, but I guess I feel like that’s more on the hiring company to decide than for you to say “no, I won’t do it”.
Basically: if I were you and I could get into a target company at an entry level doing the work I’m interested in, i would jump at it. Maybe you’ll be able to get promoted to an intermediate role faster because you know more about delivering software professionally than others hired into this role.
It's a bit weird, but I wouldn't worry about it.
In the end, level and title are just strings next to your name. Just focus on finding a good place for you; since you're starting out, growth and compensation are going to be more important than level. I talk about this more in this Q&A.
Another thing to consider is that expectations at Big Tech are generally higher than other companies - There is a reason why these companies are some of the most prestigious in the entire world. At a lot of companies, their mid-level or even senior level will map to entry-level (or the "new grad" level) at a Big Tech company like Google.
Speaking anecdotally, I have seen people with 4 years of experience get hired as an L3 at Google, which is their entry-level. And there's nothing wrong with that as everyone grows at their own pace - Your career is not a race.
Entry-level at these Big Tech companies will usually pay extremely well too; this is another reason these companies are so powerful. I worked at PayPal as my first job, and the median pay for a senior engineer there is around the median pay for an L3 at a FAANG/FAANG-equivalent company.
To sum it all up, if an opportunity makes sense for you given your priorities (you can learn how to identify this from our masterclass about team/company selection), there's nothing wrong with taking it, even if it's for a level that feels off to you.