Why is it SOV (and not SVO) in 我可以跟她约会?
Chinese is supposed to be SVO

Correct. More specifically, Chinese can be SVO or SV, plus additional components. Sometimes we omit the subject if it's obvious what the subject refers to.

&quot;约会&quot; means to date, so It's a verb I presume

&quot;约会&quot; can be a verb (go on a date/hang out) or a noun (a date). When using it as a noun, we need to use a classifier before it. &quot;我/有/一个/约会&quot;=&quot;I / have / a / date&quot;
When using as a verb, the simplest way is &quot;我/约会&quot; SV, but it doesn't make sense at all because you can't go on a date alone. So the common usage is

我/和/她/约会
I / hang out / with / her

The only difference with the english version is Chinese tend to put 和她 (adverbial modifier, which only gives more details and is omittable in a sentence) before the verb. So it's still an SV structure.