Going out on your first date with someone will usually create this type of stress: eustress

That statement is true.

In psychological field, Eustress is also being referred to as 'good stress'

Which mean that this type of stress actually would be beneficial to the general wellness of the person compared other type of stress.

When we're about to go on a date, the stress would most likely come from the expectation of what fun activities that you and your dates would do, which would release dopamine that make you feel various positive emotions.