This first strum is a straightforward strum-chunk. Here we'll strum-chunk using down strokes while playing a C chord. You're not hitting the strings hard, you're hitting them fast, being concise and accurate. It's the speed of the strum that gives swing its signature bounce. Notice that there is a little bit of space between each strum. That happens when you relax your left hand just a little bit, taking pressure off the strings to dampen them.
Remember to play through the jam track ten times even though it may seem easy. The repetition will put you firmly in the swing head space. Count this strum: ONE - two - THREE - four.