C++17 Partial Deduction Guide

The idea above is that user should still be forced to enter "int size" argument of template, but "typename T" should be deduced from the argument of constructor, is this possible?

According a note (and following examples) in this cppreference page

Class template argument deduction is only performed if no template argument list is present. If a template argument list is specified, deduction does not take place.

no, this isn't possible (not in C++17; we can hope in future versions of the standard).

If you want explicit the size and let deduce the type, the best I can imagine is pass through a good-old make_something function.

I mean something as follows (using std::size_t for the size, as in std::array and almost all STL)

template <std::size_t S, typename T>
Board<S, T> make_Board (std::vector<T> const & v)
 { return {v}; }

// ...

auto b = make_Board<3>(initialStateVector);

that should works also in C++11.