To start a crowdloan campaign, you need to specify
- ParaID (Assuming you registered as a parathread)
- Cap - the maximum number of tokens that can be contributed
- FirstPeriod - Planned start of the parachain lease
- lastPeriod - Planned end of the parachain lease
- end - the block number at which you would like to end the crowdloan campaign
Now, coming to your question, as you mentioned lease period 20, I inferred that you are planning to start a crowdloan campaign on Kusama. The next available auction on Kusama is 32nd auction that starts on April 13th. If you manage to win that auction, you have a chance to onboard your parachain after May 19th. The earliest you can onboard is during the lease period 21. Your chance to have onboarded as a parachain during lease period 20 is gone!
If you do not want to compete with the parachains which are aiming for lease period 21 onboarding, you can choose to set firstPeriod as 22 and lastPeriod as 29. You can choose to start the crowdloan anytime for any of the parachain slots in the future (each parachain slot has a range of 8 lease periods) and run it for a really long time so that you manage to win, but the contributors are stuck with your crowdloan till the end block you specify, if you do not manage to win any auction.
Would having a lower cap speed up getting into one?
Setting a crowdloan cap is a strategic decision that involves many considerations. One of them is that you should have enough tokens to be competitive and stand a chance in winning the auction. Setting a lower cap and getting maxed out will essentially freeze your crowdloan and no additional contributions can be made to it.
For an insight into crowdloan campaign strategies, check out the previous successful crowdloan campaigns on https://parachains.info/auctions/
For more info on Auctions and Crowdloans, refer to Polkadot Wiki:
https://wiki.polkadot.network/docs/learn-auction
https://wiki.polkadot.network/docs/learn-crowdloans