C++ - Is it possible to use "operator overload" without objects?

Question

What I would like to do is to use an operator such as "operator=" but without an object. I think it is not possible by default, but maybe I am missing something. A summarized code would be the following (it does not compiles, but to show the purpose);

template<uint16_t dir_>
struct Register{
   static inline void equal(uint8_t _val);    // <<--- This is valid but not what I want
   static inline void operator=(uint8_t _val);  // <<--- This is not valid, but I would like to have this syntax

};
......
Register<0x25>::equals(1);
Register<0x25> = 1;     // <<--- This syntax is nicer :) 

I have a project in which I use the "void equals(...)" syntax, but I want to have a more friendly syntax using the operators, a minimal compilable example of my current setup is next:

#include <stdint.h>

template<typename Type_, uint16_t Dir_>
struct Register {
    static inline void equal(Type_ _val) {
        *reinterpret_cast<volatile Type_*>(Dir_) = _val;
    }
};

template<typename Reg_>
struct Foo {
    
    static inline void setOn() {
        tccrA_::equal(1);
    }

    typedef Reg_ tccrA_;
};

typedef Foo<Register<uint8_t, 0x35>> Timer1;  // 0x35 is restricted, it a sample address...

int main(){
    Timer1::setOn();
}

The class Register represents a memory address and writes in it with the equal function.

The class Foo represents an entity that needs to write in a memory address, using as template argument a Register type of the previous Register template class. It uses the Register::equal function statically to avoid create a Register object in memory. Also, no object of class Foo is created, saving memory.

I want to use operator= instead of the function equal to write in the memory address, but the operator needs an object, and I don't want to create any object. It's possible to do this? This is what I say:

static inline void setOn() {
    tccrA_ = 1;
}