How to install or build GDAL 3+ on Debian buster?

You have to install it "manually" and unfortunately you have to have also proj>=6 and other dependencies.

Here is the process:

# Check Debian version (I guess you have Buster version)
lsb_release -a
#-------------------------
# OPTIONAL --> QGIS 3.10:
# add this lines to --> sudo nano /etc/apt/sources.list
deb https://qgis.org/debian-lrt buster main
deb-src https://qgis.org/debian-lrt buster main
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-key F7E06F06199EF2F2
sudo apt-get update 
apt-get install qgis qgis-plugin-grass saga 
#-----------------------------
# install dependencies
sudo apt-get install g++ sqlite3 libsqlite3-dev libtiff5-dev curl pkg-config
#-----------------------------
# install proj-7
wget https://download.osgeo.org/proj/proj-7.2.0.tar.gz
tar xvzf proj-7.2.0.tar.gz
cd proj-7.2.0
./configure --without-curl
make && make install
#-----------------------------
# Download GDAL v3.0.4 Source (ex. 3.0.4)
cd /home/user # return to your home folder
sudo wget download.osgeo.org/gdal/3.0.4/gdal304.zip
unzip gdal304.zip
cd gdal-3.0.4
./configure
sudo make clean && sudo make && sudo make install

# Set LD_LIBRARY_PATH so that recompiled GDAL is used
export LD_LIBRARY_PATH=/usr/local/lib

## Check if it works
gdalinfo --version

As you can see: here it is GDAL within Debian buster