Are there non trivial maps from $H\mathbb{Z}$ to $MGL$?

Let $ k$ be a field of characteristic $ 0$ . Let us denote by $ \mathbf{1}_{k}$ the sphere spectrum. Let $ MGL$ be the algebraic cobordism spectrum.

We have the following diagram

$ $ H\mathbb{Z}\leftarrow \mathbf{1}_{k}\rightarrow MGL$ $

My question is the following:

Are there non trivial maps $ H\mathbb{Z}\to MGL$ such that the above triangle commutes?