Are you running any other code before you initialize this circuit? If so, change it so it's the very first thing you do out of reset. The resistor idea mentioned above is good, even a high value like 100k would be fine.
A more global way would be to delay the application of 12V to the relay circuit by gating it with a FET.
You could probably have achieved the same thing using a single chip, the TPIC6B595.
Anyway the 74HC245 has a /OE (NOT OUTPUT ENABLE) pin which you could, by default, pull HIGH. After the initial start up, pull it LOW using a free GPIO pin. This should suppress the random output while you set all the outputs for the relays to LOW. You may still need pull down resistors on the ULN2803 inputs.
Thanks all for your time and comment. # OE to GPIO pin and pulldown ULN2803 is good idea which I will consider in next update after test. because my PCB is already pinted.
Unfortunately I have 03 number of 74HC245 at input / output and I was expected these type of issue so I add tip switch on #OE pin which can pullup or down.
Input flickering I controll by add some delay in setup (program). I will update here after apply the above recommendations.
My PCB and input scheamatic is attached may some one improve further.
You will need to put bypass capacitors, 0.1uF at each of the ICs to help with glitch suppression and filtering your power supply.
Even a 10uF or 100uF capacitor at the point on the PCB where you connect power would help with smooth operation.
This is actually standard practice for all digital circuits. The issue you had would not
have occurred with anyone else's circuit because they typically add the 10uF cap across the 5V power rail and the 0.1uf at each IC BEFORE they even install the ICs.
This has been standard practice since the days of TTL in the early 70's. You will find
it in Don Lancaster TTL COOKBOOK
(first published June, 1969) (the year I enlisted in the Air Force on a whim)
(this is what my copy looked like when I had it).
2021-1969=52 years people have been doing what you just discovered.
Convenient that the 10k resistor is already there.
In fact, that is the only reason that the resistor would be there.
Well, except for the general advice to use such a resistor to tie any control line - such as the "DIR" pin of the 74HC245 - pin 1 - to a fixed level "just in case" you might find a reason to later add some additional functionality.
The big question is why is the OP using a 74HC245 rather than a 74HC595?
R3 should be replaced by a wire - CMOS inputs can tolerate direct connection to supply or ground and this will be least noise-sensitive.
The '245 is not performing any function here (in fact its possibly the reason for the proble), the ULN2803 can take logic inputs directly, no need to buffer as only ~1mA per pin is needed.
In fact adding the '245 means that when the inputs to the '245 float its outputs will be undefined (potentially jumping around from low <-> high). The 2803's inputs take current and thus don't float so directly connecting them to the microcontroller will prevent flickering during the power-up/boot sequence.
And yes every chip need decouplng - this is always assumed with electronics.