Every time her and I are around him, he is constantly making her laugh.
Bro! He's her brother ffs! He's only known her all her life and probably played a big part in developing her sense of humor as a child, what did you expect?
It's neither 'alpha' Or beta behavior.
Guys, seriously, short periods of one type of behavior or another does not the 'alpha' or beta' make!
Such terms are more like the terms 'North' and 'South', they are simply directions relative to one's position. You can't go more North than 'true north' but there are plenty of 'degrees' in between the two. Personally I consider myself a sigma
The 'ideal man' is a good balance of all traits, and a man in control of his own decisions is in a much better position to choose to make 'alpha' type decisions when they think it's appropriate.
But the chances of 'demonstrating your alphaness' to a girl on the first date is virtually impossible, beyond having a strong frame and a strong fit body, how else does one 'display alphaness'? Once you get her into bed is really your first true 'opportunity' to demonstrate your 'alpha nature' and you either keep it up/going or you lose frame and fold.
IME you'll get much further if you can make a girl laugh with you than you can by just 'looking good' and pretending to be the 'strong silent type' -- yeah some girls like that type of guy but girls are usually hopeless at communicating attraction with guys, esp with the SST so chances are that Stoic Sam is going home alone anyway!
IME most girls will keep talking to a guy who can make them laugh. Although it's easier said than done, the more you talk to a girl the faster you can ascertain her game and whether the 'attraction' is mutual. Many women will string men along just for the validation, aka 'cockteasing'
If you can't get into her head and then, get her into your frame, the chances are high that you won't be getting into her pants either.