Boosting current on Genuino MKR1000 digital pin output
Although this is mostly a duplicate of "How do I increase the drive current from the arduino digital pins?" as kindly commented already, there is another point to address in your question.

You said:


  I am trying to switch on a G5Q Relay on a Genuino MKR1000. I am able to do it using VCC (3.3v)


The lowest coil voltage G5Q relay has a nominal 5V coil - not 3.3V. The fact that yours operates at 3.3V is not guaranteed and will be affected by things including temperature, internal wear etc. The G5Q datasheet I linked above shows that Omron guarantee the relay will operate at 75% of nominal coil voltage = 3.75V for a 5V coil. Therefore, as I said, your relay is not guaranteed to operate at 3.3V.

You may also find this previous question interesting, about operating relays at reduced voltages: "Is it OK to use a lower voltage to operate a relay coil than rated coil voltage?"

Therefore your situation seems to require:  


an suitable external driver (e.g. transistor) and freewheeling diode, to drive the relay coil (see the first linked question above) from the 3.3V digital output of your board; and
a suitable power supply voltage for your relay.

That means using a 5V supply for a 5V relay, if you expect reliable operation. From researching your MKR1000 board, I see that 5V is available when the board is powered via its USB or Vin connectors. This could be used to supply a 5V relay coil (assuming a suitable current rating of that power supply). Don't use the 3.3V supply which you mentioned, to directly power a 5V relay.

However when the board is powered from an attached LiPo battery, then only the 3.3V supply voltage is available. A boost regulator could be added to generate 5V from that 3.3V input, and the generated 5V could be used to power a 5V relay. I could not find documentation stating how much current your board can supply at 3.3V (to power a 5V boost regulator and relay) in that situation. The answer will be related to the 3.3V regulator IC (AP7215-33YG, according to the board schematic) and how much current the board already uses, from the 600mA maximum which that regulator can supply according to its datasheet.


So in summary: The way forward depends on how you intend to power your board. I just wanted to highlight that powering a 5V relay from 3.3V (even when you think it works, as you stated) can result in problems.