At the time to build a transaction with cardano-cli using the command cardano-cli transaction build, you can use the input parameters --invalid-before SLOT or --invalid-hereafter SLOT where invalid-before refers to the time that transaction is valid from (in slots), and invalid-hereafter to the time that transaction is valid until (in slots).
Notice that if you don't set a valid range the default will be "all the time".

You can get this info using cardano-cli transaction build --help
An example of this would be the following command (shown by Lars in lecture 3). Check https://github.com/kindofdev/plutus-pioneer-program-iter3/blob/main/code/week03/testnet/grab.sh
cardano-cli transaction build \
--alonzo-era \
--testnet-magic 1097911063 \
--change-address $(cat 02.addr) \
--tx-in 18cbe6cadecd3f89b60e08e68e5e6c7d72d730aaa1ad21431590f7e6643438ef#1 \
--tx-in-script-file vesting.plutus \
--tx-in-datum-file unit.json \
--tx-in-redeemer-file unit.json \
--tx-in-collateral 18e93407ea137b6be63039fd3c564d4c5233e7eb7ce4ee845bc7df12c80e4df7#1 \
--required-signer-hash c2ff616e11299d9094ce0a7eb5b7284b705147a822f4ffbd471f971a \
--invalid-before 48866954 \
--protocol-params-file protocol.json \
--out-file tx.body
here the tx is invalid before slot 48866954. In plutus:
Constraints.mustValidateIn $ from $ slotToBeginPOSIXTime def 48866954
In your case you should use --invalid-before $CURRENT_TIME_SLOT
If you are wondering how to get a slot number for Cardano testnet given a posixtime, here you have a way to do it.
How to convert posixTime to slot number on Cardano Testnet