You might find this answer of @LondonAppDev which worked for him by doing the following in Dockerfile:

FROM python:3.10

ARG AUTHED_ARTIFACT_REG_URL
COPY ./requirements.txt /requirements.txt

RUN pip install --extra-index-url ${AUTHED_ARTIFACT_REG_URL} -r /requirements.txt

Then, run this code to build your Dockerfile:

docker build --build-arg AUTHED_ARTIFACT_REG_URL=https://oauth2accesstoken:$(gcloud auth print-access-token)@url-for-artifact-registry

Check out this link for the full details of his answer.