In general, it is not possible to delete the initial portion of a file - you can only truncate a trailing portion of it.
Newer Linux kernels, however, support punching holes into files for specific filesystems, using the fallocate()
system call. There is a corresponding utility that can be used for the same purpose, although you need a relatively recent version (2.21 or later) of the util-linux
package for hole punching support to be included in that utility.
Keep in mind that hole punching is still relatively new and kernel bugs still pop-up - you might be better off just cleaning up your filesystem to free some space.