Manchester United did shown some good changes in a first match with Arsenal and I consider it is a signal of their promising future with Ruben Amorim. They cleary did not get good results in two matches so far but it's not right to sack Ruben Amorim immediately as it only results in another crisis for Manchester United. Let's give him at least one first half of season, then can consider of sack decision around winter transfer season.

I still think that giving Ruben Amorim this full season to prove his ability is a best choice for Manchester United. If they don't do this, and sack him in middle of season, they will return to impatient approach in previous seasons and it's hard to convince other head coaches to join their club after Ruben Amorim.
And I haven't seen any change at Manchester United since those two games. So far, Manchester United haven't scored a goal purely through their game plan, with one goal coming from a Fulham own goal. They also lost 1-0 to Arsenal, which was a poor result.
While this is just the beginning, it's worth remembering that in their next matches after Burnley, they face Manchester City and Chelsea. Even if Manchester United can beat Burnley, and I don't think they can beat Manchester City and Chelsea in their next matches, their poor record could continue if results aren't good, and failure in their next matches could seriously jeopardize Amorim's position as manager.
And I see Manchester United, instead of recovering from last season, which was their worst in three decades, still stuck in the same problems, and this is something that would be difficult for anyone other than the legendary manager Alex Ferguson to overcome.