AJo bad beat

Better to have pushed this preflop?
NL Texas Hold'em Trny:17269802 Level:6 Blinds (75/150)
Table Three-Table(510972) Table #1 (Real Money)
Seat 5 is the button
Total number of players : 10
Seat 1: MP ( $2470 )
Seat 2: MP1 ( $1220 )
Seat 3: MP2 ( $1275 )
Seat 4: roppi ( $4565 )
Seat 5: Button ( $2920 )
Seat 6: SB ( $2480 )
Seat 7: Hero(BB) ( $1800 )
Seat 8: UTG ( $3615 )
Seat 9: UTG+1 ( $2635 )
Seat 10: UTG+2 ( $7020 )
Trny:17269802 Level:6
Blinds (75/150)
** Dealing down cards **
Dealt to Hero(BB) [ Ac Jd ]
UTG folds.
UTG+1 folds.
UTG+2 folds.
MP folds.
MP1 calls [150].
MP2 folds.
roppi folds.
Button calls [150].
SB calls [75].
Hero(BB) checks.
** Dealing Flop ** [ 5h, Jc, 2h ]
SB checks.
Hero(BB) bets [600].
MP1 folds.
Button folds.
SB will be using his time bank for this hand.
SB is all-In [2330]
Hero(BB) is all-In [1050]
** Dealing Turn ** [ 3h ]
** Dealing River ** [ Th ]
Hero(BB) shows [ Ac, Jd ] a pair of jacks.
SB shows [ 5d, Kh ] a flush, king high.
SB wins 680 chips from side pot #1 with a flush, king high.
SB wins 3900 chips from the main pot with a flush, king high.
Player Hero(BB) finished in 10 place
Hero(BB) has left the table.