Is this a mammoth file? How does this file grow? Is it appended or perhaps.. prepended to? Is this a log?
If this was a file that were going to grow, and some code creates or manages this file; .. maybe I would store where that place is, the line num, for later use .. elsewhere. That is.. maybe you could keep metadata<.i> about where the place you want is. like..
Maybe your file is in a named textfile.log, and it's the only file in a dir.. You could touch the line number in that dir.. so you'd create an empty file named (for example) ./3456, then you can do an ls -I textfile.log, what you get back would be the line num of where to open textfile.log
Depending on what you're doing, this could prove slower- and then maybe faster.