How to use docker postgres as base image in Dockerfile?

Question

I need to run a golang web server with postgres. I wanted to put everything into one Docker image but don't know how to run database in the background.

Dockerfile

# Build Backend
FROM golang:1.16.3-alpine3.13 AS server-builder
WORKDIR /go/src
COPY backend .
RUN go build -o server .

FROM postgres:13.2-alpine
WORKDIR /wol-server
ENV POSTGRES_PASSWORD root
ENV POSTGRES_USER root
ENV POSTGRES_DB root
COPY --from=server-builder /go/src/ /wol-server/
COPY ./docker_postgres_init.sql /docker-entrypoint-initdb.d/docker_postgres_init.sql
CMD ["./server"]

If I run server this way, database won't start, I tried a few different things but could not get it working.

FYI, here are some file of the official postgres docker image:

• Dockerfile
• entrypoint