Question about Kärcher SC 3 EasyFix

No, this is not normal, there may be a slight odour when you first use it, as with any appliance, but not a strong odour. I advise you to return the appliance to the seller.

slight smell only at the beginning

No, that's not normal. Mine doesn't smell like burning plastic. It is often used.

Every device that heats up during operation will initially burn off and outgas the residue remaining from the manufacture upon first use. That is normal. I can't remember if mine emitted a particularly strong smell during first operation, but that's probably because I expect such things to happen and don't think it's noteworthy when they do. Now it does have a specific smell when it operates, kind of like a hair dryer when you first turn it on, but it's not bad or of plastic, more like a heated metal surface. Your device is probably fine. The smell should go away soon. Don't operate it unsupervised until you're sure it's ok.