We compute initial data for single and binary black holes in the trumpet topology, and data for quasi-stationary inspiral binary black holes, using a method proposed by Baumgarte. The Baumgarte's method does not require a decomposition of singular and regular parts of the pucture. We modify the Baumgarte's method suitable for the poisson solver of our COCAL code - Compact Object CALculator. We show tests for a boosted and single black hole following Baumgarte's work, then show results for trumpet puncture initial data of binary black holes in circular orbits.