We need to tell the parser to process the header line for us. We specify that as part of the CSVFormat, so we'll create a custom format like this:

CSVFormat csvFormat = CSVFormat.RFC4180.withFirstRecordAsHeader();

Question code used DEFAULT, but this is based on RFC4180 instead. Comparing them side-by-side:

DEFAULT                               RFC4180                       Comment
===================================   ===========================   ========================
withDelimiter(',')                    withDelimiter(',')            Same
withQuote('"')                        withQuote('"')                Same
withRecordSeparator("\r\n")           withRecordSeparator("\r\n")   Same
withIgnoreEmptyLines(true)            withIgnoreEmptyLines(false)   Don't ignore blank lines
withAllowDuplicateHeaderNames(true)   -                             Don't allow duplicates
===================================   ===========================   ========================
                                      withFirstRecordAsHeader()     We need this

With that change, we can call get(String name) instead of get(int i):

User currentUser = new User(
        Integer.parseInt(csvRecord.get("id")),
        csvRecord.get("first"),
        csvRecord.get("last"),
        csvRecord.get("city")
);

Note that CSVParser implements Iterable<CSVRecord>, so we can use a for-each loop, which makes the code look like this:

String path = "./data/data.csv";

Map<Integer, User> map = new HashMap<>();
try (CSVParser csvParser = new CSVParser(Files.newBufferedReader(Paths.get(path)),
                                         CSVFormat.RFC4180.withFirstRecordAsHeader())) {
    for (CSVRecord csvRecord : csvParser) {
        User currentUser = new User(
                Integer.parseInt(csvRecord.get("id")),
                csvRecord.get("first"),
                csvRecord.get("last"),
                csvRecord.get("city")
        );
        map.put(currentUser.getId(), currentUser);
    }
}

That code correctly parses the file, even if the column order changes, e.g. to:

last,first,id,city
doe,john,1,austin
mary,jane,2,seattle

I ended up just doing this:

CSVParser csvFileParser = CSVFormat.DEFAULT.parse(new FileReader(new File("/path/to/csv")));

Still blows my mind that all articles and official apache documentation show examples using a method that doesn't appear to exist.