Why SlidesApp alone won't get you there
SlidesApp, the standard Apps Script service, gives you full read-write access to slide content — shapes, text, speaker notes, layouts — but it has no method that produces an image. There is no getAsPng(), no export(), nothing. The first time I hit this, I spent twenty minutes grepping the autocomplete before accepting the gap is real.
The escape hatch is the Advanced Slides Service, which wraps the Google Slides REST API v1. You enable it under Extensions > Apps Script > Services > Slides API. Once it's on, the global Slides object appears in your script, and Slides.Presentations.Pages.getThumbnail(presentationId, pageObjectId, options) returns a ThumbnailImage resource containing a contentUrl pointing at a PNG.