What should I do regarding that 1st MNC is CTS and 2nd MNC is TCS.

I have worked a small start up for 24 days. I don't have experience letter for that. After that I have joined a MNC as a fresher. After 3 years I am switching to another MNC. They are asking for Experience letter for the Start Up where I have worked for 24 days. Pervious start up company's HR is telling that they can't provide experience letter for 24 days but they will approve everything. But new MNC's HR (Where I got selected) are not ready to forward without experience letter. I have all proof without the letter. In that situation what should I do. Create an experience letter or miss the opportunity ?