Could eliminating all taxes and only creating new money theoretically work? Imagine you had the opportunity to found a new country from scratch (in 2020). 
Value exchange would be digital, where only the state can create new currency units. 
Instead of relying on income tax and/or indirect taxes, there would be no form of tax but instead the government would rely on increasing the overall supply of the currency to perform welfare redistribution, such as providing Universal Basic Income. 
(note: UBI was my choice in this example since it simplifies welfare redistribution, making the question clearer)
An example:
Year 1: Initial currency units: 100. Government creates 10 more units (10%) and pays it out as UBI 
Year 2: Init. units: 110. Government creates 11 more units (10%) and pays it out as UBI 
Year 2: Init. units: 121. Government creates 12.1 more units (10%) and pays it out as UBI 
...
Each year the value of the currency is lessened due to inflation, so more money has to be generated.
Would this work if the country was completely isolated? 
If so, would it still work if international trade were a factor?
FOLLOW-UP QUESTION:
As far as I know, money was initially created as a means of value exchange, not necessarily a means of storing value. 
Since most existing answers highlight (rightfully so) that high inflation rates lead to people not using a currency to store value, but resorting to USD or similar, wouldn't it be plausible that they would still use the currency for everyday transactions, simply because it is universally recognised, thus leading to higher ease of use?
It would not work.
Historically speaking, governments that try to fund their operations primarily via the printing press experience not just inflation but hyper-inflation. Why? Well, one explanation is that without taxes nobody has any reason to want the government's currency. You can try to force people to use it, but that just encourages black marketeering.
Another way to look at it is that a policy of funding the government by printing money is equivalent to funding the government entirely with taxes on holding currency. But since the tax only applies to currency, and not gold, or land, or massive stockpiles of cigarettes, people have an incentive to avoid holding onto money at all costs. No matter the current price of cigarettes, using your spare cash to buy cigarettes for barter later on will always seem like a good deal because the cigarettes are more likely to maintain their value than the cash. But if no one wants cash, by law of supply and demand the value of cash should plummet.
Edit for the benefit of pedants: I am not saying that any &quot;inflation tax&quot; will automatically destroy the value of a currency. I am saying that people need reasons to hold your currency which are strong enough that they'll tolerate the inflation tax—and the larger the de facto tax on holding currency, the better people's reasons for doing so need to be. In the normal world, taxes are a key source of demand for fiat currency, take that away and the system stops working.