There were integrated colleges (although about 80% of black graduates in 1900 graduated from a "black college").

I am going to use 1920, because that was a census year, so it is possible to get some statistics, for "early 20th century" . The total US population in 1920 was 106 million. 95 million White, 10.5 million Black and 0.5m Other.

https://www.russellsage.org/sites/all/files/blau_ehrenberg_tables%20figures.pdf

In 1920 about 12% of African Americans graduated from high school, about 28% of European Americans.

In 1920 about 2% of African Americans graduated from college, about 7% of European Americans.

(These numbers are percentages of the age cohort that could graduate in 1920, not of the total population).

https://www.russellsage.org/sites/all/files/Fischer_Hout_Tables%20Figures.pdf

So, about 3,000 African Americans graduated from college in 1920 and about 95,000 European Americans. (Just taking % graduates as a % of total population and dividing by 70 years average life span, to get the college graduation cohort – not very precise but roughly indicative.)

The "Other" category in 1920 consisted of American Indians and South Pacific Islanders. They had just slightly lower college graduation rates than blacks so roughly 143 graduates in 1920.

So, about 3% of college graduates were non-white 95 years ago, whereas 10.4% of the population was non-white.

The overall numbers of male and female college graduates were almost equal in 1920. (Male graduates outnumbered female from 1930 – 1980, then female graduates began to outnumber males). (Don’t know if this was the case for Black college students in 1920?)

In 1900 20% of black college graduates had graduated from “white” colleges and 80% from “black” colleges, but don’t know what that was looking like in 1920.

Ivy League colleges were among the earliest colleges to enroll and graduate non-white students:

1665, The first non-white to graduate from Harvard. Charles Cheeshahteaumuck from the Wampanoag American Indians.

1828 1st African American to graduate from Dartmouth. 4th African American to graduate from any US university.

1857 1st African American to graduate from Yale.

1869 First black to earn a degree from Harvard Law School (later becomes 1st black judge in Massachusetts).

Besides the Ivy League Colleges, many other colleges and universities, particularly in the North, were integrated in the early 20th century. Oberlin in Ohio is well known as one of the early integrated colleges.

Middlebury College in Vermont had a couple of African American graduates by this point, including Alexander Twilight in 1823 (the first African American graduate of any US college/university) and Mary Annette Anderson (1899, valedictorian, first black woman admitted to Phi Beta Kappa). You can get a fuller picture here: http://www.jbhe.com/chronology/