How to install Cozy Audiobook Player in Ubuntu 20.04 without Flatpak

There is no need to create a deb-package manually.

The Cozy Stable Releases PPA is already available.
It provides deb-packages for Ubuntu 20.10 (groovy, EOL), 21.04 (hirsute) and 21.10 (impish, development) – here Cozy may be installed as simple as

sudo add-apt-repository ppa:cozy-team/cozy
sudo apt-get update
sudo apt-get install cozy

Installation on Ubuntu 20.04 LTS needs some hacks. You will need to manually install libhandy-1-0, and install updated versions of python3-peewee and python3-mutagen (otherwise cozy won't load chapters in m4b audiobooks):

sudo add-apt-repository ppa:apandada1/libhandy-1
sudo apt-get install libhandy-1-0

cd ~/Downloads
wget -c http://old-releases.ubuntu.com/ubuntu/pool/universe/p/peewee/python3-peewee_3.13.1+dfsg-1_amd64.deb
sudo apt-get install ./python3-peewee_3.13.1+dfsg-1_amd64.deb

wget -c http://archive.ubuntu.com/ubuntu/pool/universe/m/mutagen/python3-mutagen_1.45.1-2_all.deb
sudo apt-get install ./python3-mutagen_1.45.1-2_all.deb

sudo add-apt-repository ppa:cozy-team/cozy
sudo sed -i "s/focal/hirsute/" /etc/apt/sources.list.d/cozy-team-ubuntu-cozy-focal.list
sudo apt-get update
sudo apt-get install cozy

Then you can launch Cozy from dash or by using com.github.geigi.cozy command.

Note: This answer works for Ubuntu and its official flavors. In some derivatives of Ubuntu, the repository is saved in cozy-team-cozy-focal.list instead of cozy-team-ubuntu-cozy-focal.list.

It seems that OP does not want to use the PPA, which can be found in N0rbert's answer. There is a way to directly generate the .deb package from the source without using the PPA.

1. Install the build dependencies.

   sudo apt-get update
   sudo apt-get install git build-essential appstream debhelper desktop-file-utils libgranite-dev libdazzle-1.0-dev meson libgtk-3-dev python3 python3-pip python3-setuptools python3-distro python3-requests python3-tz python3-gst-1.0 python3-cairo python3-apsw sed
   

   Ubuntu 20.04 LTS does not provide libhandy-1, so we need to build it locally using sources from Ubuntu 21.04:

   sudo apt-get install debhelper-compat gtk-doc-tools libgirepository1.0-dev libgladeui-dev libglib2.0-doc libgnome-desktop-3-dev libgtk-3-doc libxml2-utils valac xvfb
   cd ~/Downloads
   wget -c http://archive.ubuntu.com/ubuntu/pool/main/libh/libhandy-1/libhandy-1_1.2.0.orig.tar.gz
   tar -xf libhandy-1_1.2.0.orig.tar.gz
   cd libhandy-1-1.2.0
   wget -c http://archive.ubuntu.com/ubuntu/pool/main/libh/libhandy-1/libhandy-1_1.2.0-1.debian.tar.xz
   tar -xf libhandy-1_1.2.0-1.debian.tar.xz
   rm libhandy-1_1.2.0-1.debian.tar.xz
   
   dpkg-buildpackage -uc -us -d
   sudo apt-get install ../gir1.2-handy-1_1.2.0-1_amd64.deb ../libhandy-1-0_1.2.0-1_amd64.deb ../libhandy-1-dev_1.2.0-1_amd64.deb
   

2. In Ubuntu 20.04, manually download a recent version of python3-peewee and python3-mutagen (in later versions of Ubuntu, you can install it from the repositories.),

   cd ~/Downloads
   wget -c http://old-releases.ubuntu.com/ubuntu/pool/universe/p/peewee/python3-peewee_3.13.1+dfsg-1_amd64.deb
   wget -c http://archive.ubuntu.com/ubuntu/pool/universe/m/mutagen/python3-mutagen_1.45.1-2_all.deb
   

   Install them

   sudo apt-get install ./python3-peewee_3.13.1+dfsg-1_amd64.deb
   sudo apt-get install ./python3-mutagen_1.45.1-2_all.deb
   

3. Install all the runtime dependencies

   sudo apt-get install gobject-introspection python3 python3-distro python3-gi-cairo python3-requests python3-packaging python3-tz python3-mutagen python3-gst-1.0 python3-gi python3-cairo python3-apsw file libgstreamer1.0-0 libgstreamer-plugins-base1.0-0 gstreamer1.0-plugins-good gstreamer1.0-plugins-ugly gstreamer1.0-plugins-bad gstreamer1.0-libav gir1.2-granite-1.0 gir1.2-dazzle-1.0
   

4. Download the source from GitHub:

   cd ~/Downloads
   git clone https://github.com/geigi/cozy.git -b 1.2.0
   

5. Download the debian/ directory from http://github.com/apandada1/cozy/tree/deb-dir and place it inside the source directory of cozy.

   cd ~/Downloads
   git clone https://github.com/apandada1/cozy -b deb-dir debian
   mv debian/debian cozy/
   

6. Now build the .deb package and install it with

   cd ~/Downloads/cozy
   dpkg-buildpackage -uc -us -b
   
   sudo apt-get install ../cozy_1.2.0_all.deb