Yes as the title suggests some dates and times have been announced for the alpha tests, posted on the PSO2 Facebook page.
■ First test
August 18 (Thu), 16:00 to 23:00
August 19 (Fri), 18:00 to 23:00
■ Second Test
August 23 (Tuesday) 16:00 to 23:00
■ Third Test
August 26 (Fri) 16:00 – 27 (Sat) 23:00
Bonkohara notes that these dates may change, presumably this depends on the outcome of these tests.
You can find a translation of the alpha test schedule here. Of note is that initial tests will only concern the forest and lobby, with the 3rd test scheduled to add the “Volcano Cave” area seen in screenshots. They will be adding more players at each stage of the test, so good luck to all those who applied!