Need to set an output pin without it going LOW during initalization
Arduino sketches are actually (somewhat constrained) C programs.  As such, what is true for C is usually true for sketches.  In C, a segment of code usually ends with a ";".  It matters not if there are two (or more) of these on a single line.  The computer will execute the segment before the first ";" first and the segment after the first ";" second.

In this case you are setting a register inside the Atmel processor on the Nano to the "out" direction.  So it will force the associated pin to what ever the data in already set up in that pin's data register.  Then you are setting that pin's data register to high or 1.

Instead, try setting the data register to 1 before setting the direction register to "out".  Do this by switching the order of the code segments.

In case this does not work.  Or in case you find the relays acting randomly on power up, consider the relay driver inputs to be high impedance and susceptible to any noise prior to the Nano taking control of the relay driver control pins.  In such a case, consider adding pull up resistors small enough to ensure the inputs of the relay drivers are held at a known voltage but high enough such that the Atmel processor in the Nano can easily over power the pull up resistor when necessary.