Apply Entity Framework migrations when using ASP.Net Core in a Docker image

I have an ASP.Net Core application which uses Entity Framework with Sqlite. I am building a Docker image to deploy this.

The ASP.Net Core application runs fine when debugging with VS Code, but when running in a Docker container I receive an error:

SqliteException: SQLite Error 1: 'no such table: MyTable'.

I figured this is because I need to run the Entity Framework migrations when I build the Docker image. I have added dotnet ef database update to my Dockerfile, which looks like:

FROM microsoft/dotnet:sdk AS build-env
WORKDIR /app

COPY *.csproj ./
RUN dotnet restore

COPY . ./
RUN dotnet publish -c Release -o out

RUN dotnet ef database update

FROM microsoft/dotnet:aspnetcore-runtime
WORKDIR /app
COPY --from=build-env /app/out .
ENTRYPOINT ["dotnet", "MyApplication.dll"]

The image builds without errors. However, when I create a container and look at the database, it is empty with no tables.

What is the correct way to set up a database with Entity Framework when building a Docker image?