Hey, I was going thorugh my magic cards again (yes, to look for an abusive way to use them) and I found the shallow grave....it arises one question Though...

When I special summon the monster on the turn, face down, can I flip it face up? I think due to game mechanics I cannot. Still, I wanted to ask in this post.

no, you cannot change the battle position of a monster in the same turn you summon it. unless its battle position is changed due to an effect

You cannot manually change the Battle Position of a monster in the same turn it is summoned, if it declared an attack or has already had its position changed that turn...as said many times before...you would have to use Book of Taiyou, Desert Sunlight or some other card to change the position...