Can we prove that all CFLs can be recognized by a Turing Machine in polynomial time?
There are several misconceptions in this question and too many to cover in a comment.


We do not know that $\mathrm{P}=\mathrm{R}$ or that $\mathrm{NP}=\mathrm{RE}$. In fact, we know that both of these things are false. The time hierarchy theoreom tells us that both $\mathrm{P}$ and $\mathrm{NP}$ are strictly contained within the recursive languages.
$\mathrm{P}$ is not the class of languages accepted by any old deterministic Turing machines: they're DTMs running in polynomial time. Similarly, $\mathrm{NP}$ languages are accepted by NTMs running in polynomial time.
Without time bounds, the class of deterministic TMs and the class of nondeterministic TMs accept exactly the same languages: you can simulate nondeterminism deterministically but exponentially slower.
Also, we know that $\mathrm{REG}\subsetneq\mathrm{CFL}$, which is consistent with what you wrote but a stronger statement. Exercise: can you give an example of a context-free language that is not regular?
Another nitpick: you write "$\mathrm{P}\subseteq\mathrm{NP}$ or $\mathrm{P}=\mathrm{NP}$"; the second statement is already included in the first.