I think that your issue is more related to the conversion from an object to an array, to be able to iterate on it. There are multiple ways to do that:

1 - You can use Object.entries() as @hgb123 recommended you:

const myObject = { a: 1, b: 2, c: 3};
const myArray = Object.entries(myObject);
console.log(myArray);

2 - You can get the keys of the object using Object.keys(), as @Gandzal recommended you, and iterate on the returned array:

const myObject = { a: 1, b: 2, c: 3};
const myKeys = Object.keys(myObject);
console.log(myKeys);
const myArray = myKeys.map(key => [key, myObject[key]]);
console.log(myArray);

3 - Or you can use Array.prototype.reduce() on the array returned by Object.keys():

const myObject = { a: 1, b: 2, c: 3};
const myArray = Object.keys(myObject).reduce((arr, key) => [...arr, [key, myObject[key]]], []);
console.log(myArray);

Whatever method you choose, iterate on an array, and display its results is easy after the conversion:

const data = {
  "2020-09-19": [
    {
      end: "2020-09-19T10:30:00Z",
      start: "2020-09-19T06:52:10Z",
      user: "rakul",
    },
    {
      end: "2020-09-19T18:30:00Z",
      start: "2020-09-19T10:30:00Z",
      user: "jeet",
    },
    {
      end: "2020-09-20T02:30:00Z",
      start: "2020-09-19T18:30:00Z",
      user: "rahul",
    },
  ],
  "2020-09-22": [
    {
      end: "2020-09-20T10:30:00Z",
      start: "2020-09-20T02:30:00Z",
      user: "rakul",
    },
    {
      end: "2020-09-20T18:30:00Z",
      start: "2020-09-20T10:30:00Z",
      user: "jeet",
    },
    {
      end: "2020-09-21T02:30:00Z",
      start: "2020-09-20T18:30:00Z",
      user: "rahul",
    },
  ],
};

const List = props => Object.entries(props.data).map(([date, items]) => (
      <div key={date}>
          <strong>{date}</strong><br/><br/>
          {
              items.map((content, index) => (
                  <span key={index}>
                      start: {content.start}<br/>
                      end: {content.end}<br/>
                      user: {content.user}<br/><br/>
                  </span>
              ))
          }
      </div>
  ));

ReactDOM.render(
  <List data={data} />,
  document.getElementById('example')
);

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/16.8.6/umd/react.production.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/16.8.6/umd/react-dom.production.min.js"></script>

<div id="example"></div>

You'll need to either insert BR tag appropriately in the resulting string, or use for example a PRE tag so that the formatting of the stringify is retained:

var data = { a: 1, b: 2 };

var Hello = React.createClass({
    render: function() {
        return <div><pre>{JSON.stringify(data, null, 2) }</pre></div>;
    }
});

React.render(<Hello />, document.getElementById('container'));

Working example.

Update

class PrettyPrintJson extends React.Component {
    render() {
         // data could be a prop for example
         // const { data } = this.props;
         return (<div><pre>{JSON.stringify(data, null, 2) }</pre></div>);
    }
}

ReactDOM.render(<PrettyPrintJson/>, document.getElementById('container'));

Stateless Functional component, React .14 or higher

const PrettyPrintJson = ({data}) => {
    // (destructured) data could be a prop for example
    return (<div><pre>{ JSON.stringify(data, null, 2) }</pre></div>);
}

Or, ...

const PrettyPrintJson = ({data}) => (<div><pre>{ 
    JSON.stringify(data, null, 2) }</pre></div>);

Working example

Memo / 16.6+

(You might even want to use a memo, 16.6+)

const PrettyPrintJson = React.memo(({data}) => (<div><pre>{
    JSON.stringify(data, null, 2) }</pre></div>));