Do I claim cryptocurrency from "Pi Network"? It is not live yet and has no value yet. It's in the mining stage only.

No, not until you have a value for the cryptocurrency. Pi coin is not yet available to trade on any cryptocurrency exchange or trading platform. The price of PI has yet to be established.

Since there is no value, you are in the preliminary stages of the business, or startup cost position.  If you are mining cryptocurrency the reporting rules are as follows.

Reporting :

• For US tax, mining is an income producing activity and is therefore classified as a business.
• Most home miners will report their activity on a Schedule C. The mined coins will be reported as income and any associated expenses, such as utilities and depreciation of requisite fixed assets will be included.
• Larger mining operations may have other entities such as SCorp or Partnership reporting its crypto activity on K1s.
  • Two key points here:
    • Income is earned when the coins are earned and the amount reported is the USD equivalent, at the time it was earned.
    • When a miner exchanges one currency for another or converts the digital currency to a physical currency (e.g., USD, Euros, etc) this act also makes them a trader.

Start-up Expenses: You can deduct up to $5,000 in these expenses the first year your business is actually operating to produce a profit, which may be the current year even though income has not yet been achieved.  For the past several years this limit has been $5,000. You’ll have to deduct any additional start-up expenses in excess of the first year limit in equal amounts over the first 180 months (15 years) you’re in business. This is referred to as an amortization deduction and is similar to depreciation but somewhat different.  TurboTax will help you with this deduction. 

• Startup Business Tax Tips

if the coin does not exist, how can you hold it as an asset?

Or record any Date Acquired?

If you have a financial interest, then the answer to the yes/no question would be YES.