read first line from .gz compressed file without decompressing entire file

Piping zcat’s output to head -n 1 will decompress a small amount of data, guaranteed to be enough to show the first line, but typically no more than a few buffer-fulls (96 KiB in my experiments):

zcat logfile.gz | head -n 1

Once head has finished reading one line, it closes its input, which closes the pipe, and zcat stops after receiving a SIGPIPE (which happens when it next tries to write into the closed pipe). You can see this by running

(zcat logfile.gz; echo $? >&2) | head -n 1

This will show that zcat exits with code 141, which indicates it stopped because of a SIGPIPE (13 + 128).

You can add more post-processing, e.g. with AWK, to only extract the date:

zcat logfile.gz | awk '{ print $1; exit }'

(On macOS you might need to use gzcat rather than zcat to handle gzipped files.)

You could limit the amount of data you feed to zcat (or gzip -dc), then ask for the first line:

head -c 1000 logfile.gz | zcat 2>/dev/null | head -1 | read logdate otherstuff

Adjust the 1000 if that doesn't capture enough data to get the entire first line.

To just match a date from the 1st line of a zipped file - zgrep solution:

zgrep -m1 -o '^[^[:space:]]*' logfile.gz

This will output the first YYYY-MM-DD for you.