One root spans space, time, and progress, because in Hebrew they are the same axis. קֶדֶם is the front, which is also the east (where the sun rises) and the ancient past (what came before). From this single "in front / earlier" idea grow verbs for preceding, doing things early, advancing something, and making progress. The forward direction in space becomes earliness in time becomes progress in life. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
Watch the voices line up. Pa'al = simply be ahead. Pi'el לְקַדֵּם = push something else forward (promote a project). Hif'il לְהַקְדִּים = causative on time, make it happen earlier. Hitpa'el לְהִתְקַדֵּם = the action turned back on yourself, you advance. The passive binyanim are not lexicalized for this root.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.