The best evidence that the Taliban began a "lightning offensive" and overran Afghanistan is option D.
In August 2021, the Taliban launched a lightening offensive across Afghanistan. The success of this offensive surprised everyone including the Taliban.
The Taliban were able to capture most of the country including the capital in less than a month because:
the Taliban had a morale boost from the U.S. pulling out ahead of schedule
Afghan army units were surrendering to the Taliban across the nation
In conclusion, option D is correct because it shows how fast the Taliban were able to capture Afghanistan and why they were able to.