Best way to async data inserts into timescaledb
If the files are comma separated or can be converted into CVS, then use Timescale tool to insert data from CVS file in parallel: timescaledb-parallel-copy

A manual approach to insert data into hypertable can be to create several sessions of PostgreSQL, e.g., by executing psql my_database in several command prompts and insert data from different files into the same hyperatble. It is important that parallel loading will insert data into different chunks. For example, if hypertable is created with default chunks size, one chunk will fit one week of data. Thus different parallel sessions should read data from files belonging to different weeks. Otherwise, parallel execution will not perform well due to conflicts. Also you want to fit active chunks into memory.

In both cases it is good that the data are already sorted by timestamp as mentioned in the question.