I think you
can, in some (many?) cases. Whether you should or not (or... how you do it) is perhaps the deeper question.
My parents were pushed by others around them to get me recognized as gifted/advanced (or whatever the term in the 70s was). Other parents (and my parents' parents) all recognized something different, so my parents went to the school, right before I started kindergarten. They got a reassuring pat on the head by the teacher and principal. "Everyone thinks their child is unique/special/advanced, especially their first, but trust us, everyone needs this..."
School started on Wednesday, and Friday afternoon they got a call saying "lowercased should be accelerated a grade or two - he's too advanced". So I was moved up a grade - that's the only lever the school had for "advanced" and, to my knowledge, I was the only one they'd done that for in the 20+ years the school had been open. I later learned it might have been 2 grades but my dad was concerned about socialization issues. And... 1 grade was bad enough in that respect.
There were multiple programs for "behind" students - kids were taken out of class for directed reading programs, other counseling sessions, etc. But there was nothing for 'advanced' kids in our area for several years. So yeah, I think there should definitely be more recognition and support for 'gifted' students in some capacity, even if it's subtle. Perhaps moreso if it's subtle. Being visibly 'different' is difficult for a lot of kids.