Typically you will only contribute to the HSA during that year. I have one and my money does not go into it till the beginning of the year.
If I understand your question, you want to contribute to an HSA for purposes of your 2018 tax return, but your HDHP policy will not begin until on or after January 1, 2019.
In this case, you may not contribute to an HSA for 2018. This is because you were not eligible to contribute to an HSA in 2018 because you did not have any HDHP coverage at any point in 2018. NOTE: your HDHP coverage for the month is determined by your coverage on the first day of the month. That is, if you were not covered until December 2, 2018 or later, then you had no coverage in 2018.
For future reference, the reverse is true - if you had qualifying HDHP coverage in the previous tax year and you have not already contributed tha annual HSA contribution maximum for the previous year, then you can contribute directly to the HSA in the subsequent year up until the due date of the return. This sort of retroactive HSA contribution is similar in concept to making a retroactive IRA contribution if you were otherwise qualified for the previous year.
For example, you began HDHP coverage on 7/1/2018. Because of the "last-month rule", because you had qualifying HDHP coverage on December 1, 2018, you are allowed to use the full annual HSA contribution limit for 2018 (for a Single HDHP policy, this was $3,450).
Now suppose you contributed only $1,000 to your HSA in 2018. This would leave you $2,450 under the limit ($3,450 minus $1,000). You would be able to send up to $2,450 to your HSA custodian before the due date of the 2018 return (generally April 15th, 2019) and file your 2018 return showing the contribution.
NOTE: if you do this, be very sure to indicate to the HSA custodian that the contribution is for 2018 (or whatever year we are referring to), because by default, the HSA custodian will assume that the contribution made in early 2019 is for 2019, not 2018.