Upload without FTP is much easier than you might anticipate.
FTP or SSH to the root of your public webfolder and look for wp-config.php.
Make a quick backup of the file before you temper with it:
FTP: Download a copy of the file to your computer locally and rename it to wp-config.php.bak.
Then download one wp-config.php which we will temper with later on.
SSH: cp wp-config.php wp-config.php.bak
Now open the file and insert the code below at the bottom of the file.
/** Upload without FTP credentials */
Save your file and upload it again to the server (FTP).
Now your installation is good to go and you do not need FTP credentials for uploading / installing themes and plugins.