[susan53]

He came across the self defence class first. Look at the adverbial : soon afterwards.
Afterwards is an adverb which refers back to something already mentioned. So :

We had lunch, and afterwards we had coffee = We had lunch and after lunch we had coffee.

So here : I found a self defence class and soon afterwards I started kickboxing classes = I found a self defence class, and soon after I found the self-defence class, I started kick-boxing classes.