The keyboard flex only goes in the connector until it stops - that is a zero insertion force connector - so no pushing or forcing.[br]
If you managed to scratch the carbon traces on the plastic flex it may not work properly - plastic tweezers can be a good thing if you are worried about damaging it. If you remove the blue plastic from the tip of the flex cable it will not be rigid, or as thick, and will not get a good connection / or work at all.[br]
The plastic clip / clamp on the socket is mandatory - you will not get a good connection or at all without it. if it has slid off the back of the connector it is possible to put it back on with a magnifier and some tweezers - but be careful, it is easy to damage the connector.[br]
If you aren’t comfortable doing that I would take it to a local shop - once the connector is damaged it can be replaced, but you would be charged for logic board repair at a shop that knows what they are doing, and a less knowledgeable shop would want to replace the whole logic board.