early days vs period

early days and period both are nouns.

Word	Noun	Adjective	Verb	Adverb
early days	Yes	No	No	No
period	Yes	No	No	No

As nouns, period is a hypernym of early days; that is, period is a word with a broader meaning than early days:

Other hypernyms of early days include period of time, time period.

early days (noun)	period (noun)
an early period of development	a punctuation mark (.) placed at the end of a declarative sentence to indicate a full stop or after abbreviations
	the monthly discharge of blood from the uterus of nonpregnant women from puberty to menopause
	an amount of time
	the interval taken to complete one cycle of a regularly repeating phenomenon
	a unit of geological time during which a system of rocks formed
	the end or completion of something
	(ice hockey) one of three divisions into which play is divided in hockey games