Verse 3 begins with וַֽיְהִ֖י (way·hî) that comes from the word הָיָה (hayah Strong's H1961) which is defined as "to fall out, come to pass, become, be".
We can gather addition information from the following commentaries:
Ellicott's Commentary for English Readers
(3, 4) In process of time.—Heb., at the end of days: not at the end of a week, or a year, or of harvest-time, but of a long indefinite period,
Barnes' Notes on the Bible
At the end of days. - This may denote the end of the week, of the year, or of some longer period.
Gill's Exposition of the Entire Bible
And in process of time it came to pass,.... Or "at the end of days" (c); which some understand of the end of seven days, at the end of the week, or on the seventh day, which they suppose to be the sabbath day, these sons of Adam brought their offerings to the Lord: but this proceeds upon an hypothesis not sufficiently established, that the seventh day sabbath was now appointed to be observed in a religious way; rather, according to Aben Ezra, it was at the end of the year;
Cambridge Bible for Schools and Colleges
- in process of time] Lit. “at the end of days,” a phrase for a period of quite indefinite length;
Keil and Delitzsch Biblical Commentary on the Old Testament
. . . "In process of time" (lit., at the end of days, i.e., after a considerable lapse of time:
So, "after many days" could refer to the end of the week, year, or other undefined time period.
Furthermore, the Sabbath arrangement for worship had not been formally established until centuries later under the guidance of Moses. (see Exodus 20:8-10; 31:16, 17)
For a full description of the Sabbath Day see the article in the Insight on the Scriptures.