Let $c>1/2$ be an arbitrary big fixed constant. Can one prove that for all $t\geq 1$: $$\text{erf}\left(\frac{c}{t}\right) \ge \delta \, \min\left(1,\frac{c}{t}\right)$$
for some small constant $\delta>0$?
The error function $\text{erf}(z)$ is defined as
$$\text{erf}(z) = \frac2{\sqrt{\pi}}\int_0^z e^{-t^2}\mathrm dt.$$