Can I show my Coinbase balance for proof of sufficient funds at border control?

When you apply for a visa in advance, you provide a lot of paperwork for things like how much money you have access to. When you just arrive at the border for admission without visa or visa on arrival, it rarely gets to the paperwork stage. The officer looks at how long you're staying and the reason you're staying, and uses their experience and judgement to see if they make sense. Then they look at you. If everything looks consistent, they probably just stamp your passport at this point.

When do things not look consistent? When you're dressed in overalls and steel toed boots, saying you're here to sightsee for three weeks. When you're dressed in farm labourer clothes at the start of harvest season, saying you want to visit your cousin for a month or two. When you say you're here for 3 days and then going straight back where you came from, but you have 3 huge suitcases. At this point they start asking questions. These are usually about money because a big worry is that a "visitor" will end up being a stayer -- which usually means being a worker.

I've seen plenty of televised secondary interviews where people are asked about money and the officers are fine with things like "yes, there's a few thousand in the bank and I have a credit card of course" or similar mere assertions of having money. When the person being visited is going to pay for everything, sometimes they get a phone call asking them to confirm it. (A boyfriend who is going to pay for everything may mean this person intends to come and live with them not just visit them, but the questions to deal with that are not about money.) I don't think I've ever seen anyone asked for a paper bank statement on the Canadian show, but I have on the US one.

If it gets to the point where you assert you have access to all the money you need and they actually ask you to prove it with a bank statement, your Coinbase balance probably won't work. But one of the reasons for that is that very few interviews get to that point, and if yours has, some other things about your situation are making the officer wonder if you're a genuine visitor or not. Having an unarguable technicality to point to (no true bank statement, just some strange app on the phone with a supposed investment balance that we can't verify) will make it super easy for them to deny entry, if the other things make them feel that way.

What does this mean for you though? Probably nothing. Have the things all visitors should have: a return ticket, a place to stay booked or arranged for at least the first night, a credit card, a debit card that you can get local cash with. Dress as a person traveling for your reason dresses. Pre-pay what you can and bring the receipts. Having all of this should lead to the stamp long long before the "yeah but what do you have in a real bank account?" question rolls around.

https://www.ilo.org/dyn/natlex/docs/ELECTRONIC/101579/122464/F-2068595975/EEU-101579%20(EN).pdf

REGULATION (EU) 2016/399 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 9 March 2016 on a Union Code on the rules governing the movement of persons across borders (Schengen Borders Code)

Means of subsistence shall be assessed in accordance with the duration and the purpose of the stay and by reference to average prices in the Member State(s) concerned for board and lodging in budget accommodation, multiplied by the number of days stayed. Reference amounts set by the Member States shall be notified to the Commission in accordance with Article 39. The assessment of sufficient means of subsistence may be based on the cash, travellers’ cheques and credit cards in the third-country national’s possession

The answer is a crystal clear NO.

Further, Commission Decision C(2013) 1725 final of 26 March 2013 establishing the lists of supporting documents to be presented by visa applicants in Jordan, Kosovo and the United States of America -- here's the summary page to show 2013 is the latest -- Annex III which is for the USA has "Proof of sufficient means of subsistence for the intended journey" and while you are not asking for a visa, I would say it's pretty relevant the text says "– Bank account statement(s)". It does not say "Bank account or brokerage account" or such -- while 2013 certainly predates the widespread existence of Bitcoin exchanges, online brokerage accounts existed since 1995 (E*Trade) or you could say since 1982 with NAICO-NET. And yet, in their infinite wisdom, the lawmakers decided not to mention these entities even for visa applications where the decision makers have a lot more time to check the documents supplied. No way would border check accept them.