MMA can find the identity of the following integral

$$int_0^infty textrm{e}^{-(x/t)^2-t}textrm{d}t text{for $x>0$} tag{1}$$

with a Meijer G function

$$

frac{1}{sqrt{pi}}G_{0,,3}^{3,,0} left( {begin{array}{*{20}c}

{} \ {0,frac{1}{2},1} \

end{array};left| {;frac{{x^{,2} }}{4}} right.} right) tag{2}$$

```
FullSimplify(Integrate(Exp(-(x/t)^2 - t), {t, 0, ∞}), x > 0)
```

output:

```
MeijerG({{}, {}}, {{0, 1/2, 1}, {}}, x^2/4)/Sqrt(π)
```

How can be done the opposite way, i.e. I know eq.(2) but want to get eq.(1)?

MMA 12.1