Right phonetic
齐 supplies the sound — qí shifted to jǐ via palatalization, the same shift that links
加 jiā /
架 jià. Faint semantic flavour bleeds through too:
齐 means 'all level, packed together evenly', which fits the squeezing/crowding sense of
挤. Same phonetic in
济 (jì, aid) and
剂 (jì, dose).