It is hard to tell if it will work without a proper diagram, however you have some things missing. You need a large capacitor across the power input to the strip, at least 1000uF.
You also need a resistor in seriese with the strip’s data line, between 330R and 510R.
You do not say how many LEDs their actually are in that strip. They can take up to 60mA for each LED so the power supply needs a good capacity if it is going to last long.