Probably not
The intention for the film seems to have changed over time
Originally, the movie was conceived as a straight prequel to the 2007 Transformers film, showing Bumblebee's exploits on Earth during the Cold War. Remnants of this concept can be seen in Bumblebee's own prequel comic. However, this concept changed substantially during production, instead ultimately making <PERSON> depict the character's first arrival on Earth.
According to an announcement coinciding with the cancellation of Transformers 6, it was planned for a "new team" to "reset" the continuity "after" Bumblebee. I'm using lots of scare quotes because I don't really know how to interpret this paraphrase with regards to Bumblebee itself.
But it seems plausible that Bumblebee might stealthily be the beginning of the reset, rather than the tail end of the old continuity, because:
There are several discontinuities with the previous films
In the existing continuity, the Autobots arrive on Earth in the late 2000s, with The Last Knight additionally revealing that Bumblebee had first come to Earth during World War II (early to mid 1940s). Bumblebee has <PERSON>'s first arrival take place in 1987, with the rest of the Autobots joining him perhaps a few weeks afterward.
Their reasons for coming to Earth are also different. 167
In the original continuity, the Autobots came because the AllSpark was there, having been sent there by <PERSON> thousands of years ago during the fall of Cybertron. In Bumblebee, <PERSON> says nothing of the AllSpark and instead suggests Earth as a place to lie low and build up the Autobot resistance after the fall of Cybertron which is circa Earth's present day.
Furthermore, the existing continuity has Transformers appear as early as 1895 when <PERSON> is discovered frozen in the Arctic Circle, with the military organization Sector 7 keeping him locked away after that point. In Bumblebee, the members of Sector 7 seem unfamiliar with Transformers in 1987, with Dr. <PERSON> excited to study technology that according to the old continuity they would have already been reverse engineering from <PERSON> for decades.
The Transformer redesigns you mentioned also hint that Bumblebee is pursuing different avenues from the previous movies, at least in spirit if not in canon, but on their own they are not conclusive evidence of anything, since any number of in- or out-of-universe explanations are possible without affecting the official continuity.
EDIT: Looked around a bit more and apparently Bumblebee's director has stated that <PERSON> was omitted from the opening scene specifically because he was frozen on Earth at the time. However, a scene depicting the frozen <PERSON> was in fact scrapped from early cuts of the film. This seems to fit with the movie originally being conceived as a straight prequel, but being adjusted more into a maybe-soft-reboot. 837