Do Trezor wallets always generate the first account at the same index?

does the wallet always create the first account at index 0?

Yes, the wallet derivation path defaults are declared in the trezor suite wallet source code. https://github.com/trezor/trezor-suite/blob/5377ec9e20d5e37951db2ad4a8bbeca437ed8d69/packages/suite/src/utils/wallet/coinmarket/coinmarketUtils.ts#L115

{
    name: 'Bitcoin (legacy)',
    networkType: 'bitcoin',
    accountType: 'legacy',
    symbol: 'btc',
    bip44: "m/44'/0'/i'",
    decimals: 8,
    explorer: {
        tx: 'https://btc1.trezor.io/tx/',
        account: 'https://btc1.trezor.io/xpub/',
    },
    features: ['rbf', 'sign-verify'],
},
    

const result = await TrezorConnect.getAddress({
    device,
    coin: legacy.symbol,
    path: `${legacy.bip44.replace('i', '0')}/0/0`,
    useEmptyPassphrase: device.useEmptyPassphrase,
    showOnTrezor: false,
});
if (result.success) {
    return result.payload.address;
}

Is it possible for a user to generate an account at subsequent indices
if there are no funds at the previous index?

Yes, under the receive tab of the wallet. Although it shows index 0 by default, there’s a “+ More Addresses” button the users could click on and send BTC to a higher index prior to receiving anything at index 0. A user going too far ahead of the index on their own doing can complicate the way an HD wallet works due to look-ahead gaps. See https://bitcoin.stackexchange.com/a/54664/26873