Bitcoin 10 minute block time?

I understand that only when a block is confirmed is it added to the blockchain and for high value amounts you want to verify with 2 or 3 blocks generated afterwards to ensure the transfer has safely been accepted but what if I was asking someone to spend 0.01BTC on something and want to find out they've started this transaction as quickly as possible?

For values like this I'm not going to be too fussed if some people attempts a double spend as I'll simply not serve them again (much like how if someone tries the spend/refund on Paypal)

I know I could just say 'I'll assume you've sent payment' and just agree the transaction has happened and consider it fraudulent if payment isn't received within 2 blocks but I was curious if there is a slightly safer way of quickly finding they have published their intent to transfer the 0.01BTC for the mining network to pick it up?

If so, are we talking seconds in typically detecting their published transaction or is it still minutes?

If it's the latter why is this not seen as a significant limitation on Bitcoin replacing cash since cash being instant is a feature everyone relies on nearly daily.