Can I read a signal in Time domain, only inside a Time?
Not from a .mat file, NO.
For some other kinds of data files, it is sometimes possible to jump around within the file to locate the boundaries of where the times match, and then to extract only that section. This is pretty much restricted to binary files with fixed record sizes, and the search field (sweep_time) would have to be known to be sorted.
For all other file organizations, the best you can sometimes do is to read from the beginning and stop reading when you recognize that you have exceeded the last target time. But you cannot do that with .mat files or with .xlsx files; you can sometimes do it with text files such as csv files.
So... what you do instead, is to read the entire file, the way you already do, and then to extract a subset of it that matches the time range you want.
TT = table(sweep_time(:), power_array(:), 'VariableNames', {'sweep_time', 'power_array'});
mask = TT.sweep_time >= FirstTime & TT.sweep_time <= LastTime;
extract = TT(mask,:);
plot(extract.sweep_time, extract.power_array);
