Can I make the playbar appear at a specific point in the timeline?

What you describe here is possible if you know how to program Event Listeners in JavaScript or you have access to the CpExtra JS library widget for Captivate.   Be aware, this is not a free widget.

More information about CpExtra's Add Even Listener function is found here:

Event Listeners | CpExtra Help (widgetking.github.io)

Event List | CpExtra Help (widgetking.github.io)

Basically what you want to have happen is that an Action to Show Playbar is triggered when a specific slide object (e.g. a SmartShape or button) enters the slide timeline.  All of this is possible to achieve with CpExtra.

If you read through the Help files in the link above, but you feel pulling this off is still beyond you, you might choose to pay for the services of the widget developer to do it for you.  Your call.

Something like this, with an Advanced Action triggered by the On Enter slide event;

Beware: the Delay command doesn't take into account if the slide is paused somewhere.