When do infants generally enter the "clingy" stage? I feel like my son (almost 3 weeks) is starting…

When do infants generally enter the "clingy" stage? I feel like my son (almost 3 weeks) is starting to become extra clingy. He was extra fussy and wanted to be held and wouldn't go to sleep until just now only because I'm laying down with him next to me leaning against my chest..... Not that I mind, I love his little cuddles 😍. Just not sure if this is normal or something may be wrong.