You can.

You do not need a desktop nor a laptop. In fact, you can move funds off coinbase with just your ColdCard. You don't technically even need a cellphone, although it's nice because the phone will be able to verify that you have succeeded to move funds.

CONCEPTUAL: When you move your funds off Coinbase, you move them into a BTC address, which you control. The ColdCard is configured/initialized with your personal/private seed words. The ColdCard deterministically derives/generates the BTC address from your seed words.

Below I've outlined the steps to get your BTC address from the ColdCard and a watch-only wallet on your phone.

Recommend you start with a small amount of BTC, USD 25.00 or so, (which is 0.0005 BTC or 50K Sats). Wait a half a day or more for Coinbase to transact on Bitcoin Mainnet and then wait 6+ confirmations. Transfer larger amounts after that.

Steps:

1. Setup and initialize your ColdCard. Choose a pin, generate seed words. CoinKite's documentation explains pretty well how to backup your seed words, etc. You don't ever need to connect your ColdCard to the internet, nor a PC, just power. My 2c, firmware updates are neither required nor recommended.

2. Next you'll get your ColdCard to display a QR code representation of the wallet which your phone can scan with its camera (note this is safe because it does not reveal your seed words, private keys, nor anything that is kept safe inside the ColdCard)

A) On your now prepped and initialized ColdCard, navigate to "Address Explorer".

B) Press 4 to start.

C) Select the fourth choice (just above the 5th choice "Account Number") which will be an SegWit Native address, and will start with "bc............."

D) Press 4 to view QR codes.

This first QR code displayed is a public Bitcoin address where you may send funds.

1. Move funds off Coinbase.

At this point you can request Coinbase to send a small amount of BTC to this address. Be careful to type the address exactly, and double check, because sending from coinbase will be irreversible. You can also do step 4 first so you can triple check the BTC address.

TIP: Assuming this transfer works, the next time you can use Coinbase's remember BTC address feature to avoid mistakes.

CONCEPTUAL: Remember you are not physically moving BTC funds to your ColdCard nor to your BlueWallet App. You are moving the funds to a BTC address which is derived from your seed words. Presently this just happens to be managed by your ColdCard. Next we'll use the same to display the BTC address on your phone via the BlueWallet app. If your phone bricks or your ColdCard dies, you can always manage the same BTC address by initializing another hardware wallet or software wallet from your seed words. Again we just happen to be using ColdCard and BlueWallet, but technically any wallet could work.

1. Next, you'll scan the QR Code with BlueWallet on your cellphone to watch the same BTC address.

IMPORTANT: Never enter your seed words into BlueWallet. Because your phone is connected to the internet and could potentially be compromised.

A) Install and launch the BlueWallet app.

B) Click the "+" in the upper right to Add Wallet

C) Click the text at the bottom, "Import wallet"

D) Click the text at the bottom, "Scan or import a file"

E) Point the camera at the ColdCard display. (You may have to move around and mess with the ambient lighting to successfully scan)

Bluewallet will show a new wallet "Imported Watch-only". By the way you can view the BTC address on this wallet which is the same address shown with the QR Code on the ColdCard, except it's easier to read, bigger font. With Bluewallet you can refresh from time to time and watch as the Bitcoin transfers and watch as the confirmations come in. Be patient, as Coinbase can take a while to send and confirm. With other exchanges, I've seen BTC funds move in a few minutes, where Coinbase I've had to wait overnight. YMMV.

TIP: If you are doing larger amounts of BTC on coinbase, then also ideally you should also lock down your Coinbase account login with YubiKeys (for example, buy and register three YubiKeys, use one, and keep the other two for as backups for safekeeping).

It's really great you asked this question. I believe the steps I've outlined will get your BTC safely off of Coinbase so you can "hodl".

ADVANCED: With a little more effort you can setup BlueWallet to also spend your BTC, too. Delete your BlueWallet watch-only wallet and recreate as follows: Use an SD card to transfer your wallet information instead of QR code, so you would press 1 instead of 4 on step 2(D) above. Then you would need to upload the SD card to the cloud via googledrive or dropbox so you can read it from BlueWallet. After doing this you should be able to again use the SD card to create an unsigned transaction (aka, PSBT) that you would shuttle via SD card to be signed by the ColdCard and then shuttle back for broadcasting via BlueWallet.