Since you had no plan established by December 31, 2016, no 401(k) contribution is permitted for 2016. The only type of plan that can be established after the end if 2016 to receive a self-employed retirement contribution for 2016 is a SEP plan. A SEP plan can be established and a SEP contribution made to a SEP IRA up until the due date, including extensions, of your tax return for the year of the contribution. Contributions under a SEP plan are employer contributions, equivalent to a profit-sharing contribution to a 401(k).
If you establish a one-participant 401(k) plan before the end of 2017, you'll be able to make elective deferrals and a profit-sharing contribution for 2017 based on your 2017 net profit from self-employment. However, you generally cannot maintain a 401(k) plan for the same year as a SEP plan (because this is not permitted with a SEP plan established using Form 5305-SEP, as most self-employed SEP plans are), so if you establish a SEP plan to receive a contribution for 2016, you would have to terminate the SEP plan for 2017 to be able to establish a 401(k) plan.
