Can't* do that on 2 layers. Use 4 layers at least.
*) When someone says something can't be done, I tend to take it as a challenge
.
While you definitely can kludge something up and through huge amount of tedious work get it functional - possibly with narrow margins - it's not the easy way.
Funny thing is, people less experienced in PCB tend to assume that having more layers is more "difficult", more "complex", or at least super cool.
In reality, the more you have layers, the easier everything is. It feels almost cheating. Naturally, routing is far easier. Signal integrity comes easily with dedicated planes. Thermal conductivity increases.
You could always do 16 layers even for a LED blinker. Only the cost prevents this.
Luckily, 4 layer PCB is not too expensive in China anymore. So 2-layer is applicable in simple LED blinkers, and in more complex design only when you are very experienced and have a lot of time to tweak the design - exactly the opposite what people assume.