## 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?