Can a Cohen marry a single mother (who has had relations once in her life, for example, and the child’s father is Jewish)?
The single mother fits all other requirements as well as being a bat cohen.
Shulchan Aruch Even HaEzer 6:1 (all translations from sefaria.org):
A priest if forbidden from the Torah to marry a divorced woman, a harlot [zonah], or a challalah (a woman of invalid priestly lineage).
Who is deemed a "zonah" [who is forbidden to a kohen]? Whoever is not a Jewess, or who is a Jewess that had sexual relations with a man to whom she is forbidden to marry in a generally applicable prohibition, or who had sexual relations with a "chalal" (the child of a kohen and a woman who was forbidden to the kohen), even though she is permitted to be married to this man ... And similarly a man that has relations with a single woman, even though she is a lewd woman that made herself freely available, which is punishable with lashes, she does not become a zonah and she does not become invalid to a kohen, because she is not forbidden to him.
So in principle, a single woman who slept with a Jewish man who would have been allowed to marry her (and was also not a chalal (disqualified kohen)) is allowed to marry a kohen.
However, we need to clarify how we know the identity of the man the she slept with.
A single woman whom they saw having intercourse with someone, and the one who had intercourse left and they said to her: Who was this that had intercourse with you? And she said: A valid man. She is believed. Furthermore, even if they saw her pregnant and they said to her: Who impregnated you? And she said: A valid man. Behold, she is believed and she (and her daughter) are permitted to a priest. When is this so? When the place where she had intercourse was a crossroads, or at the corners of a field where everyone passes by, and most passersby are valid, and most of the city from which the passersby came from are valid. For the sages made a stringency with genealogy and required two majorities. But if most passersby would disqualify her [from marrying a priest] such as non-Jews, or mamzers or other such ilk, even though the place they came from was mostly valid, or if most of the men of the place were invalid, even though most passersby were valid, we cannot trust her and we must say: You had relations with one who would disqualify you, and you may not marry a priest. But if she does marry [a priest] she need not be divorced. And there are those who say that if she says: I had relations with a valid man, one majority alone is sufficient to make her valid, and ex post facto, even if most are invalid.
If they saw that she had intercourse or she was impregnated in the city, even if there was only one non-Jew there or one disqualified priest or someone like that, she may not be married ab initio to a priest, for all [populations] that are fixed are judged as fifty/fifty. And if she is married, she need not be divorced since she says, "I had relations with a valid one." If she was mute or deaf or if she said, "I don't know whom I had intercourse with" or if she was a minor who couldn't tell the difference between a valid one and an invalid one, this one is a doubtfully profaned woman and if she is married to a priest she must be divorced, unless there were two majorities found there who were valid. And there are those who say that even if she was impregnated in the city if the man who had intercourse went to her she may be married ab initio, since most of the city and most of its groups are valid, unless she went to him. And in general as well, when we don't know who went to whom, she may be married ab initio.
As can be seen, there are many circumstances and differing opinions that need to be taken into consideration when deciding whether we can be sufficiently certain of the man's identity to permit her to subsequently marry a kohen.
So for any practical questions, a competent rabbinic authority would need to be consulted.