It is highly unlikely you will trading crude to 'settle' the future's contract. First, see this calendar for WTI Crude Oil on CME. If this isn't the future you are trading, then you should find the similar calendar for that contract; which may be traded on a different exchange.
I'm going to use the Jul 2020 row for my examples. Also, I assume you purchase 1 contract of crude oil (CLN20). The important date is Last Trade Date which is 22 Jun 2020. This is the last day you may trade the future. Your broker will most likely force you to liquidate your position before this last trade date. You will thus not be 'settling' any contracts, physically or financially.
The First/Last Position date (which are the same date) is the date CME calculates your 'final position' for any outstanding contracts. The First/Last Notice date is the date CME notifies you have been assigned delivery: either you must deliver (number of contracts * 1000 barrels) of crude oil or you must receive (number of contracts * 1000 barrels) of crude oil. Then the First/Last Delivery date is the actual date of delivery.
Unless you are a trader at major financial institution or large multi-national company you will not be settling any contracts, even if it's a cash-settled future. Instead you will be buying and selling the futures contract in order speculate that the price will go up/down as you predict in order to profit, closing your position before the Last Trade Date of the contract.
You might (and did) ask, when and how do I profit? The answer is you profit when you sell (or buy) to close the position. If the closing occurs on 01 June 2020, then that is when you profit from your trade.
Also see this similar question.