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Just as above...If we print money and simultaneously introduce some sort of government intervention in order to increase supply/ production, then supply and demand would be 'balanced' and therefore price wouldn't go up. I must be missing something, can anyone tell me what it is?

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Yes it can. There is nothing wrong in the above. The money market equilibrium is given by equation of exchange (See Mankiw Macroeconomics pp 87) as:

$$MV=PY$$

Where $M$ is the money supply, $V$ velocity of money, $P$ price level and $Y$ output.

Solving for price level and log-linearizing we get:

$$\ln P = \ln M + \ln V - \ln Y $$

Consequently, ceteris paribus, if $M$ increases by $1\%$ and $Y$ increases also by $1\%$ then the net effect on price level will be zero. The crucial assumption is of course that $V$ remains constant otherwise there could still by inflation/deflation.

However, this is not because this would balance supply and demand - or at least not as understood in econ jargon. When people talk about balancing supply and demand they just talk about them being in the equilibrium. Aggregate supply and demand can be in equilibrium even if inflation increases. Rather here it would be more appropriate to say that both supply and demand shift to the right by amount that makes leaves the price unchanged.

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Short answer: Yes it is theoretically possible.

Long answer: Well, there are a lot of 'ifs and buts'

First, please understand there is a difference between increase supply and increase production. Production increases in response to higher or at least expectation of higher demand. Otherwise there is no incentive for producers to increase production.

Increasing supply is also a confusing. You can increase supply by moving up along the supply curve (assuming of course that supply curve is upward sloping and not vertical). Here the supply increases with increase in prices. But what you are perhaps referring to is an exogenous rightward shift of the supply curve. Here the supply increases for every given price level. This can very well be through government intervention such as improved access to better technology. This is the story so far about supply side.

Increasing money supply (printing money is one way of this) is a demand side intervention which shifts demand curve rightward. So you can imagine a case when you shift both curve such that equilibrium price remains unchanged.

But please note that this requires a strong assumption that aggregate supply curve is upward sloping. This in turn happens under assumptions such as wage rigidity, price stickiness, etc.

This is a much simplified view as in general equilibrium there are plenty of more assumptions that need to be qualified.

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    $\begingroup$ I think overall this answer makes some good points about distinction between movement along supply curve and shifts of supply curve, but I must point out that I dont think the following holds "there is a difference between increase supply and increase production". Aggregate supply is literary given by production function so $AS=Y=F(K,L)$ then in the long run of course $F(K,L)$ is just vertical line while in short run it also depends on price. But point is that aggregate supply is literary defined in terms of output so any change is supply has to imply change level of output $\endgroup$ – 1muflon1 Nov 17 '20 at 13:39
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    $\begingroup$ @1muflon1: Yes that is correct. I didn't word this properly. What I meant was that govt intervention increasing production could also be interpreted as govt expanding expenditure, for example by buying more defense equipment. That would be a demand side intervention not supply side. Clearly what I have written is not clarifying this. $\endgroup$ – Dayne Nov 17 '20 at 14:08

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