Short answer
Technically yes, but almost every DIY scheme fails the "randomness" test. Human brains, birthdays, phone numbers, SHA-256 of "a sentence I made up" — none of these are valid entropy sources. Attackers run scanning scripts that hash every English phrase, popular password, Bible passage, and Linux dictionary entry — your "self-invented" private key gets swept within seconds. If you must generate manually, use a physical entropy source: flip a fair coin 256 times, or use cryptographic dice 99 times.
Why brains are bad RNGs
Private-key security depends on 256 bits of true randomness — every bit 50/50 independent. Brains can't do this. Psychology research has shown that humans asked to "say a random number sequence" unconsciously avoid repetition, prefer odd numbers, and avoid extreme values. These biases compress the actual search space from 2^256 to maybe 2^30 — about a billion guesses, scannable in hours.
The brain-wallet massacre, 2013-2017
Around 2013, brainwallet.org let users input a memorable phrase, SHA-256 it, and use the output as a private key. Attackers built scanning bots that hashed Wikipedia article titles, popular song lyrics, Bible verses, Reddit comments, common passwords. Estimates of total brain-wallet losses by 2017 exceeded $250 million.
The crucial insight: an attacker doesn't need to find your phrase; they only need any phrase that happens to control a non-empty address. Out of billions of users, plenty would use predictable phrases. The attacker scans all addresses and waits for matches.
The physical-entropy method
If you want to generate a 12-word BIP-39 mnemonic by hand on an offline computer: roll a casino-grade die 50 times and record each result, or flip a fair coin 128 times. Type the binary or decimal into the iancoleman/bip39 tool (in offline mode), and it derives the corresponding mnemonic. Coldcard's "dice rolls" feature does this natively. The result is real 128-bit entropy, equivalent to what any hardware wallet's RNG would produce.
The simpler answer
Just let your hardware wallet generate it. Ledger, Trezor, Coldcard all use certified true-random number generators on their secure elements. The "DIY entropy" pattern is for paranoid edge cases, not normal users.
Further reading: Private key, Hardware wallet.