The bridge at Delhi and the terminus became operational on January 1st, 1867.
The first attached scan is from the official reports to the Indian Secretary of State on May 24th, 1864, where the speaker reports to Lord Ripon that the bridge works at Delhi are still incomplete. Link to the full report: click here . These are records of the parliamentary proceedings in England.
The second scan is from the 1904 Administration Report on the Railways in India, which was an annual publication by the Railway...
more... Board. This publication contains details of ALL the railway lines, dates of inauguration, doubling, tripling etc for EVERY railway line constructed in the subcontinent till that point, and also the finances, details about ongoing projects, surveys etc for that year. This report was actually published EVERY year till 1964, when IR stopped the publication. Some issues between 1893 and 1907 are publicly available on Google, while the other issues can be accessed in overseas libraries. This report mentions that the section to Delhi terminus was opened on January 1st, 1867.
click here