I doubt you will find a tech company, at least in Silicon Valley where you will have employees actually use a punch card to punch in and out, when they get into work and leave for the day, because thats obsurd. But fostering a trusting environment amongst your employees is still something startups are strunggling with, and that's a fundamental problem that will ultimately affect the quality of their output, and your product or service.
As a founder, instead, you should inspire leadership, rather than project authority, which will lead to building loyalty amongst the team, an essence that intangible and invaluable. Forging and nurturing trust in your startup is akin to a general in a battle who builds the moral of his soldiers, which is the advantage beyond the size of the unit. It's what makes one underdog soccer team of 11 players defeat another team, its trust and belief.
So, as a leader, the way you project yourself to your team explicitly through your words, and implicitly through your behavior. So how do you forge trust in your startup?
Trust your employee
Give your employees some autonomy and faith, rather than block their access to Facebook during work-hours, or check your watch when they arrive into the office. The saying happy wife happy life, the same applies in the workplace, happy employee happy office, and giving employees trust that they will finish their set tasks.
Set expectations, but let employees manage their time
This is the mantra of an agile startup team, they can come in whenever as long as they do what is expected of them. Meaure performance in output, not input. After all, you hire employees so they can tell you what to do, not so you can tell them what to do. If you don't have an employee where you can set expectations without having to put a leash on him or her, take a close hard look at whom you bring into your team.
Its a career, not a job for the employee
That is the message you should convey, and working in a startup, no doubt you will have to burn the midnight oil every now and then, so you will end up spending a lot more time with your colleagues than you do with your family. Beyond assigning tasks, have lunches, help employees with opportunities to take a short-course to continue building their technical education, and help them follow their passions. They need to feel like their skills are relevant, and providing an encouraging environment where opportunities to learn are presented.
Get to be more personal with each employee
You can also forge personal relationships with employees. I personally wouldn't hire someone I can't have a beer with (doesn't have to be alcohol but someone you can relax with outside of work), and getting to know each employee, their origin story, whether they are married, have kids, birthdays. Of course there are boundaries in employer/employee relationships, but being able to take an interest in your employee builds greater camaraderie.
Be honest and transparent
Nothing to bring down morale in a company than to have dishonesty or an opaque structure. Instead, foster trust and confidence through including everyone in decisions, democratically, and providing clear vision, goals and progress of how the company is going. The same goes for individual performances, forego yearly reviews and instead provide candid feedback to each member (and make sure it goes both ways).
When you pivot in the project, let the team understand why you did, even if they don't completely agree with it. If your company's burndown is at a critical stage, let them know, include them rather than hide it from them.